Question

A rectangular rug is 24 feet long and 10 feet wide. A rhombus design is formed inside the rug by joining the midpoints of each side of the rectangle. What is the length of each side of the rhombus?

Answer 1

In all geometry problems, drawing a diagram is most helpful.

The half-side lengths are 5 feet and 12 feet.

By the Pythagorean Theorem, the hypothenuse, or side length of the rhombus is therefore

sqrt(5^2+12^2)=sqrt(169)=sqrt(13^2)

= 13 feet.

See diagram below.