b Before using Guess, Check, and Revise, write an equation using the given information.
A
aEquation: 81= 4x+1/2x
Area: 18 square feet
B
b 3 feet by 6 feet
Practice makes perfect
a We are told that the tatami is made of four identical rectangular mats and one square mat. Let x be the area of each rectangular mat and y be the area of the square mat. We can find the area of the tatami mat A by adding these areas.
ccccc
Tatami & & Rectangular & & Square
A & = & 4x & +& bWe are also told that the area of the square mat is half the area of one rectangular mat and that the area of the tatami mat is 81 feet squared.
81=4x+ 1/2x
We can now solve this equation for x.
The area of one rectangular mat is 18 square feet.
b Before using Guess, Check, and Revise, we will write an equation using the given information. Let l be the length of a rectangular mat and w be the width. It is given that the length is twice the width.
l =2w
The area A of a rectangle can be found by multiplying the length and the width.
A= l * w ⇒ A= 2w * w
Let's substitute A=18 and try to solve for w.
Now, we can arbitrarily choose values for w (Guess) and substitute them into the equation. Then, we will evaluate the equation for each value (Check). Finally, we will Revise by trying different values for w until we have w^2=9.
Guess
Check
Revise
w
w^2
=
1
1^2
1
2
2^2
4
3
3^2
9
Our work in the table shows that the width of the rectangle is 3 feet. Substituting w=3 into our equation for l will give us the length of one rectangular mat.
