Question

I'm kinda stumped on this one.. How do you start?

Answer 1

Devin wants to have equal amounts of room on all four sides of his ping pong table. A 5ft by 9ft table is placed in the center of a rectangular room that has an area of 221 square feet. What is the width of the clear space Devin will have on all sides of his table? Show your work.

Answer 2

This is what I put:

A = 221 sq ft
(2x + 9)(2x + 5) = 221

FOIL: 4x^2 + 28x + 45 = 221
4x^2 + 28x - 176 = 0

Simplify: x^2 + 7x - 44 = 0

Plug into the quadratic formula: -b+/- √b^2 - 4ac / 2a
a = 1 b = 7 c = -44

Plug in the numbers: -7+/- √7^2 - 4(1)(-44) / 2(1) x = -7+/- √7^2 - 4(1)(-44) / 2(1)
x = -7+/- √49 + 176 / 2
x = -7+/- √225 / 2

Break into 2 problems: x = -7 + 15 / 2 and -7 - 15 / 2
x = 4 or -11

Width can't be a negative so, x = 4