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46. PROBLEM SOLVING Tatami mats are used as a floor
covering in Japan. One possible layout uses four
identical rectangular mats and one square mat, as
shown. The area of the square mat is half the area of
one of the rectangular mats.
Total area = 81 ft2
a. Write and solve an equation to find the area of
one rectangular mat.
b. The length of a rectangular mat is twice the
width. Use Guess, Check, and Revise to find
the dimensions of one rectangular mat.

Respuesta :

calculista

Answer:

Part A) The area of one rectangular mat is 18 ft^2

Part B) The length of the rectangular mat is 6 ft and the width is 3 ft

Step-by-step explanation:

see the attached figure to better understand the problem

Part A) Write and solve an equation to find the area of  one rectangular mat.

Let

x ------> the area of a square mat

y ------> the area of one rectangular mat

we know that

[tex]x+4y=81[/tex] -----> equation A

[tex]x=\frac{1}{2} y[/tex] -----> equation B

substitute equation B in equation A and solve for y

[tex]\frac{1}{2}y+4y=81[/tex]

[tex]\frac{9}{2}y=81[/tex]

[tex]y=81*2/9=18\ ft^2[/tex]

therefore

The area of one rectangular mat is 18 ft^2

Part B) The length of a rectangular mat is twice the  width. Find  the dimensions of one rectangular mat.

Let

L -----> the length of rectangular mat

W -----> the width of rectangular mat

The area of rectangular mat is

[tex]A=LW[/tex]

[tex]A=18\ ft^2[/tex]

so

[tex]18=LW[/tex] ----> equation A

[tex]L=2W[/tex] -----> equation B

substitute equation B in equation A and solve for W

[tex]18=(2W)W[/tex]

[tex]18=2w^2[/tex]

Simplify

[tex]9=w^2[/tex]

square root both sides

[tex]W=3\ ft[/tex]

Find the value of L

[tex]L=2(3)=6\ ft[/tex]

therefore

The length of the rectangular mat is 6 ft and the width is 3 ft

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