Question

A rug has an area of 48 square feet. Two similar rugs have in the areas of 108 square feet in 192 square feet. In each rug, the length is 1 1/3 times the width. Which of the following could be the dimensions of the one of the rugs? Mark all that apply.

Answer 1

Let
x-----------> the length of a rug
y-----------> the width of a rug

we know that
1 1/3---------> (1*3+1)/3----------> 4/3
x=(4/3)*y

case a) area = 48 ft²
48=x*y--------> 48=(4/3)*y*y-------> 48=(4/3)*y²-----> y²=48*3/4
y²=36--------> y=6 ft
x=(4/3)*6-----> x=8 ft
The rug dimensions are 8 ft x 6 ft

case b) area = 108 ft²
108=x*y--------> 108=(4/3)*y*y-------> 108=(4/3)*y²-----> y²=108*3/4
y²=81--------> y=9 ft
x=(4/3)*9-----> x=12 ft
The rug dimensions are 12 ft x 9 ft

case c) area = 192 ft²
192=x*y--------> 192=(4/3)*y*y-------> 192=(4/3)*y²-----> y²=192*3/4
y²=144--------> y=12 ft
x=(4/3)*12-----> x=16 ft
The rug dimensions are 16 ft x 12 ft

The rug dimensions are
8 ft x 6 ft
12 ft x 9 ft
16 ft x 12 ft

Pick the one(s) that are on your list