GRE Sample Test 5 Quantitative Reasoning 2

Let w = the width. Thus, the length is w + 4. Since the diagonal of a rectangle forms a right triangle whose legs are the sides of the rectangle, we can use the Pythagorean theorem: ${\mathit{w}}^2+{\left(\mathit{w}+4\right)}^2$ = ${20}^2$
→ ${\mathit{w}}^2+{\mathit{w}}^2$ + 8w + 16 = 400
→ $2{\mathit{w}}^2$ + 8w + 16 = 400
→ ${\mathit{w}}^2$ + 4w + 8 = 200
→ ${\mathit{w}}^2$ + 4w − 192
= 0 → (w + 16)(w − 12) = 0 → w = 12 (since w must be positive), and the length = 16. Therefore, the rectangle’s area is 16 × 12 = 192.