Polynomial Factoring Please Help!

Question

A picture is 11 inches longer than it is wide. if the area of the picture is 900 in.² .find its dimensions

Answer 1

w(w + 11) = 900

w² + 11w - 900 = 0

1(-900) = -900

What two factors of -900 add up to 11?

-9 and 100? Not even close.

Ahhh, 36 and -25.

w² + 36w - 25w - 900 = 0

w(w + 36) - 25(w + 36) = 0

(w - 25)(w + 36) = 0

For the left side to equal 0, w - 25 or w + 36 has to equal 0.

w - 25 = 0

w = 25

25 + 11 = 36

w + 36 = 0

w = -36

Because we measure using positive numbers, we disregard this "answer."

The length is 36" and the width is 25".