Answer:
x = 20 ft
Area of the living room = 400 ft²
Step-by-step explanation:
From the picture attached,
Length of rug = (x - 3) ft
Width of the rug = (x - 9) ft
Area of the rectangular rug = Length × Width
= (x - 3)(x - 9)
187 = (x - 3)(x -9)
187 = x² - 12x + 27
x² - 12x - 160 = 0
x² - 20x + 8x - 160 = 0
x(x - 20) + 8(x - 20) = 0
(x - 20)(x + 8) = 0
x = -8, 20
Since, measure of 'x' can't be negative, measure of x will be 20 ft.
Therefore, area of the square living room = x²
= (20)²
= 400 ft²
