Skip to main content

2005 AMC 10A Problem 4

Problem 4 of 25EasierGeometry

A rectangle with a diagonal of length xx is twice as long as it is wide. What is the area of the rectangle?

Answer choices

Show solution

Solution

Let the width be w,w, so the length is 2w.2w. Then x2=w2+(2w)2=5w2,x^2 = w^2 + (2w)^2 = 5w^2, giving w2=x25.w^2 = \dfrac{x^2}{5}. The area is w⋅2w=2w2=25x2.w \cdot 2w = 2w^2 = \dfrac{2}{5}x^2. Thus, the correct answer is B.
AoPS wiki

Tagged: rectangle · Pythagorean Theorem · area

More practice