Question

The equation w(w + 6) = 40 represents the area of a rectangle where w represents the width. What are the dimensions of the rectangle?

Answer 1

The dimensions are thus 4 by 10 units

Explanation:

Rewrite w(w + 6) = 40 in standard quadratic form ax^2 + bx + c = 0:

w^2 + 6w - 40 = 0

This factors as follows:

w^2 + 6w - 40 = 0 => (w + 10)(w - 4) = 0.

Solving for w, we get w = 4 (and also the unhelpful w = -10).

The width of the rectangle is 4 and the length is 4 + 6, or 10.

The dimensions are thus 4 by 10 units, with area = 40 units^2