We are interested in the dimensions of a certain square. A rectangle has length twice the side of this square and width three units less than the side of this square. If the two areas are equal, what are the square's dimensions (w x h)?

QUESTION POSTED AT 06/12/2019 - 02:14 PM

Answered by admin AT 06/12/2019 - 02:14 PM


We don't need the length AND width of the square.  One number
will be enough for an answer, because all sides of a square have
the same length.  Let's call that number ' M ' (for 'mystery number').

-- The area of the square is  M² .

The question says that ...
-- The length of the rectangle is  2M .
-- The width of the rectangle is  (M - 3) .

Therefore ...
-- The area of the rectangle is  (2M)(M - 3)  =  2M² - 6M .

The question also says that ...
-- The areas of the square and the rectangle are equal:

So                                            2M² - 6M = M²

Subtract  M²  from each side:    M² - 6M = 0

Divide each side by  M :            M  -  6  =  0

Add  6  to each side :                 M  =  6 .


Check:

Assume ... Side of the square = 6

Then ...
Area of the square = 6² = 36 .
Length of the rectangle = (6 x 2) = 12
Width of the rectangle = (6 - 3) = 3
Area of the rectangle = (12 x 3) = 36

                 36  =  36                  yay! 

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Related questions

Leon verified that the side lengths 21, 28, 35 form a Pythagoreom triple using this procedure

Answer:

The correct answer is  25

ANSWERED AT 28/01/2020 - 01:08 AM


QUESTION POSTED AT 28/01/2020 - 01:08 AM

The distance from the center of a round table top to the edge of the table top is 4 ft. What's the area of the table top?

L X W = A. So, if the top of the table is 4 ft, you need to find the sq. route of 4. (HINT: the sq. route can be doubled to equal the area.

ANSWERED AT 28/01/2020 - 01:08 AM


QUESTION POSTED AT 28/01/2020 - 01:08 AM

The area of a circle is 2,826 square centimeters. What is its diameter?

Formula to find the area of circle is:

a=πr² Where a= area and r= radius of the circle.

Given area: a=2,826 square centimeters.

So, plug in a=2,826 in the above equation to get r.

2826=πr²

 \frac{2826}{\pi} = \frac{\pir^{2}}{\pi}  Dividing each sides by π.

  \frac{2826}{3.14} =r^{2}  Since π=3.14

900=r²

√900=r

r=30

Since the diamter is twice the radius.

Hence, diameter= 2*30= 60.

So, the diameter of the circle is 60 centimeters.

900=

ANSWERED AT 28/01/2020 - 01:07 AM


QUESTION POSTED AT 28/01/2020 - 01:07 AM

The sum of the measures of the interior angles of a triangle is equal to _____.

180 degrees I mean I do not know how to really explain it its based on the amount of sides a shape has and the sum of all 3 interior angles is 180

ANSWERED AT 28/01/2020 - 01:06 AM


QUESTION POSTED AT 28/01/2020 - 01:06 AM

Find the diagonal of a square whose sides are of the given measure. 7 square root of 3

I encourage you to draw in the diagonal. The diagonal of a square will create a triangle with the sides of the square. Specifically, this is a right triangle as the angles of a square are right angles by definition.

Use the Pythagorean theorem: a^2 + b^2 = c^2. In this case, sides a and b are each 7sqrt(3), and c is the diagonal of the square.
a^2 + b^2 = c^2
(7sqrt3)^2 + (7sqrt3)^2 = c^2
294 = c^2
c = sqrt(294) = 7sqrt(6)

ANSWERED AT 28/01/2020 - 01:05 AM


QUESTION POSTED AT 28/01/2020 - 01:05 AM

Lines which are drawn on a map or a globe to show the heights of given specific areas are called??

It's longitude and latitude.

ANSWERED AT 28/01/2020 - 01:02 AM


QUESTION POSTED AT 28/01/2020 - 01:02 AM

Circumference is44 so what is the area?

C (circumference ) = 2 x pi x r 
so 44 = 2 x 22/7 x r 

r = (44/2) / 22/7 
r = 7 
so area = 22/7 x r^2 
= 22/7 x 7^2 
= 22x7 = 154sq in

ANSWERED AT 28/01/2020 - 01:02 AM


QUESTION POSTED AT 28/01/2020 - 01:02 AM

Kirsten built a rectangular corral with a fence on three sides.A side of the barn served as a short side od the corral.She used 130 m of fencing . The length of the corral was 20 m longer than the width . Find the dimensions of the corral. Choices for the width : 25, 30 , 35 EXPLAIN

Answer:  Second option is correct.

Step-by-step explanation:

Since we have given that

Let the width of corral be 'w'.

Let the length of corral be 'w+20'

Perimeter of corral = 130 m

As we know the formula for "Perimeter":

Perimeter=2l+w\\\\130=2(w+20)+w\\\\130=2w+40+w\\\\130=3w+40\\\\130-40=3w\\\\90=3w\\\\\dfrac{90}{3}=w\\\\w=30\ m

so, width of corral = 30 m

Length of corral = 30+20 = 50 m

Hence, Second option is correct.

ANSWERED AT 28/01/2020 - 01:01 AM


QUESTION POSTED AT 28/01/2020 - 01:01 AM

James is constructing a circle circumscribed about a triangle. He has partially completed the construction, as shown below. What should be his next step in the construction? Triangle DEF is shown with two sets of intersecting arc markings on either side of side EF. A line segment is drawn through each set of intersecting arc markings and through side EF. Another segment is drawn through side DE and two more sets of intersecting arc markings. Connect the arc markings to angle E to find another bisector Use the compass to find the perpendicular bisector for side DF Connect three arc markings to determine the vertices form the triangle Use the circumcenter to determine the center of the circle

The correct answer is:


Use the circumcenter to determine the center of the circle .


Explanation:


The steps James has completed have constructed the perpendicular bisectors of two sides of the triangle, DE and EF. The point where the perpendicular bisectors of the sides of a triangle meet is the circumcenter of the triangle. This is also the center of the circumcircle, or circumscribed circle.


We need to extend these bisectors so that they intersect. We then set our compass on this point and set the width from this center to any vertex of the triangle. This will be the radius of the triangle; we draw the circle and are finished.

ANSWERED AT 28/01/2020 - 12:59 AM


QUESTION POSTED AT 28/01/2020 - 12:59 AM

Find the circumference and area of the circle having a given diameter of d = 13 cm

Circumference of circle = pi*diameter = 13pi cm

Area is pi*d^2/4 = pi*13^2/4 = 42.25pi cm^2.

ANSWERED AT 28/01/2020 - 12:58 AM


QUESTION POSTED AT 28/01/2020 - 12:58 AM

Find the circumference and area of the circle having the given diameter of d=13 cm.

The circumference of a circle can be found from the formula: 2 \pi r, where r is the radius (half of the diameter). 
2 x 3.1415 x 6.2 = 40.84cm

ANSWERED AT 28/01/2020 - 12:57 AM


QUESTION POSTED AT 28/01/2020 - 12:57 AM

What is the unit rate of y=-x/6

-1/6 The x is coefficient is negative and is 1/6

ANSWERED AT 28/01/2020 - 12:51 AM


QUESTION POSTED AT 28/01/2020 - 12:51 AM

What is the unit rate of y= -x/6

Y = -x/6 

y = (-1/6)*(x)

hope thsi will help you 

ANSWERED AT 28/01/2020 - 12:51 AM


QUESTION POSTED AT 28/01/2020 - 12:51 AM

Terri is analyzing a circle, y2 + x2 = 36, and a linear function g(x). Will they intersect? y2 + x2 = 36 g(x) graph of the function y squared plus x squared equals 36 x g(x) −4 −4 −2 −2 2 2 Yes, at positive x-coordinates or zero Yes, at negative x-coordinates or zero Yes, at negative and positive x-coordinates or zero No, they will not intersect

Answer:

The graph of the circle and function g(x) intersects at the positive and negative x-coordinates as well as at the origin.

Step-by-step explanation:

The equation of circle is given as:

x^2+y^2=36

also the graph of the function g(x) is given by:

We are given a set of values in a table as:

  x         g(x)

−4       −4

 −2        −2

   2          2

Hence, the function g(x) could be computed with the help of slope intercept form of a equation as:

y=mx+c; where m denotes the slope of the line and c denotes the y intercept.

when x=-4 g(x)=y=-4

-4=-4m+c

also when x=-2 then y=g(x)=-2

-2=-2m+c

on solving the above two equations using elimination method we get,

m=1 and c=0

hence, y=g(x)=x

Now we are asked tgo find whether the graph of the circle and g(x) intersect each other or not.

Clearly from the graph we could see that the graph of the circle and function g(x) intersects at the positive and negative x-coordinates as well as at the origin.


ANSWERED AT 28/01/2020 - 12:50 AM


QUESTION POSTED AT 28/01/2020 - 12:50 AM

Is the expression x^3 * x^3 * x^3 equal to x^3*3*3?

No. 
x^3 * x^3 * x^3 > x^3*3*3
x^3 * x^3 * x^3 = 19683
whereas  x^3*3*3 = 7.626 (rounded to 3 decimal places)

ANSWERED AT 28/01/2020 - 12:49 AM


QUESTION POSTED AT 28/01/2020 - 12:49 AM

Fractions- seven over twenty equals?

7/20 is equal to 0.35 or can also be equal to 35% of the whole.

ANSWERED AT 28/01/2020 - 12:49 AM


QUESTION POSTED AT 28/01/2020 - 12:49 AM

Triangle ABC has vertices of A(-6, 7), B (4, -1), and C (-2, -9). What is the length of the median from angle B?

Answer:  The length of the median from angle B is 8 units.

Step-by-step explanation:  As shown in the attached figure, A(-6, 7), B(4, -1) and C(-2, -9) are the vertices of ΔABC.

We are to find the length of the median BD from angle B to side AC.

Since BD is the median on side AC. So, D will be the mid-point of side AC.

Therefore, the co-ordinates of the point 'D' are

\left(\dfrac{-6+(-2)}{2},\dfrac{7+(-9)}{2}\right)=\left(\dfrac{-8}{2},\dfrac{-2}{2}\right)=(-4,-1).

Now, the length of median BD is equal to the distance between the vertex 'B' and the point 'D'.

Therefore, the length of median BD calculated using distance formula is

BD=\sqrt{(-4-4)^2+(-1+1)^2}\\\\\Rightarrow BD=\sqrt{64+0}\\\\\Rightarrow BD=\sqrt{64}\\\\\Rightarrow BD=8.

Thus, the length of the median from angle B is 8 units.

ANSWERED AT 28/01/2020 - 12:48 AM


QUESTION POSTED AT 28/01/2020 - 12:48 AM

The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?

Answer:

B

Step-by-step explanation:

ANSWERED AT 28/01/2020 - 12:47 AM


QUESTION POSTED AT 28/01/2020 - 12:47 AM

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

The answer is 4x cm < h < 10x cm.

The third side of the triangle is greater than the difference of the lengths of the other two sides (h > 7x cm - 3x cm) and it is less than the sum of the lengths of the other two sides (h < 7x cm + 3x cm). Therefore:
h > 7x - 3x
h < 7x + 3x

This can be expressed as:
7x cm - 3x cm < h < 7x cm + 3x cm
⇒ 4x cm < h < 10x cm

ANSWERED AT 28/01/2020 - 12:44 AM


QUESTION POSTED AT 28/01/2020 - 12:44 AM

Which fraction is equal to 2/3

4/6 , 6/9 would be 2 examples

ANSWERED AT 28/01/2020 - 12:44 AM


QUESTION POSTED AT 28/01/2020 - 12:44 AM

Does it help to remember and/or list out your square roots

It is a good thing to remember. Of course, not all, but some basic numbers that appear all the time such as the numbers from 2 to 13 should be remembered as they appear in numerous assignments and tests.

ANSWERED AT 28/01/2020 - 12:40 AM


QUESTION POSTED AT 28/01/2020 - 12:40 AM

Does it help to remember and/or list out your square roots

If you are really good at memorizing things the larger the number the harder to remember but for basic ones such as 2 squared =4 4 squared =16 3 squared =9 and so on

ANSWERED AT 28/01/2020 - 12:40 AM


QUESTION POSTED AT 28/01/2020 - 12:40 AM