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.
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
