Quadratic equations

Question

The length of a rectangle exceeds its width by 5 inches. Find the length of the rectangle if its area is 126 square inches.

Answer 1

If the length of the rectangle is L and the width W, then L= W +5. The area of the rectangle is

(W+5) x W = 126.

This leads to W² + 5W = 126.

Subtract 126 from both sides to get W² +5W -126 = 0.

This is a quadratic equation

This can be solved using the quadratic formula -b ± √b² - 4ac/2a.

There are two solutions, W = 9 and W = -14. Only the positive root makes sense.

So, the width is 9 inches and the length is 14 inches.

Answer 2

width = w

length = w + 5

area = length * width

126 = w(w+5)

w^2 + 5w - 126 = 0

(w+14)(w-9) = 0

w = 9

length = w + 5 = 14