Question

A rectangular room has a 10ft by 8ft rug in the center such that the distance from the edge of the rug to the wall is the same on all four sides. If the area of the room is 288 square feet, find the distance the rug is from the wall.

The answer I got was 13ft away, can someone check me on that?

Answer 1

You are correct if rounding to the nearest whole number.

I got 12.69 so if you round up, you will get 13 (see below)

Explanation:

X*Y = 288

(X-a)*(Y-a) = 10 * 8 = 80

X-a = 10

Y-a = 8

a = Y-8 = X-10

(X-10) * X = 288

X^2 - 10X = 288

X^2-10X-288= 0

quadratic equation

`X = (10 +/- √(100 - (4)(-288)) )/(2)`

X = (10 + 35.38)/2 =22.69 (technically it would have 2 answers, but we only want to evaluate the positive answer)

a = X- 10 = 22.69- 10 = 12.69 which would round up to 13 if you are rounding to the nearest whole number.

HOPE THIS HELPS!!!