Question

46. PROBLEM SOLVING Tatami mats are used as a floor

Answer 1

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

$x+4y=81$ -----> equation A

$x=\frac{1}{2} y$ -----> equation B

substitute equation B in equation A and solve for y

$\frac{1}{2}y+4y=81$

$\frac{9}{2}y=81$

$y=81*2/9=18\ ft^2$

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

$A=LW$

$A=18\ ft^2$

so

$18=LW$ ----> equation A

$L=2W$ -----> equation B

substitute equation B in equation A and solve for W

$18=(2W)W$

$18=2w^2$

Simplify

$9=w^2$

square root both sides

$W=3\ ft$

Find the value of L

$L=2(3)=6\ ft$

therefore

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