a living room floor consists of an area and hardwood. the area of the rug is 187 square feet. what is the area of the entire living room. (i'm attaching a picture for the rest of the problem) 20 points and brainliest if you answer correctly.

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