Quadratic Equations: Completing the Square

Question

The length of a rectangle is 13 m longer than its width and the area of the rectangle is 400 m². Find the exact dimensions of the rectangle.

Answer 1

Helen,

Are you sure the problem said the length was 13 more than the width? Maybe someone misheard it, and it is really 30 + width?

if it is 30, then it is straightforward: You know what the formula for Area is: it is Length * Width.

Lets call the width w. Then the length is (30 + w).

Area is w(30+w). And we know that is 400. So...

w² + 30w = 400

add (30/2)² to both sides

w² + 30w + 225 = 400 + 225 = 625

(w+15)² = 625

(w+15) = sqrt(625) = 25

w = 10

and you can solve for length.