A rectangle has a perimeter of 10 and a diagonal of length square root{15}. What is its exact area(as radicals if there are any)

Answer 1

Let L = length and W = width

L² + W² = 15 (Pythagorean theorem)

2(L + W) = 10 => L + W = 5 => L = 5 - W

Substitute

(5 - W)² + W² = 15

This quadratic will need to be expanded, collected and solved by the quadratic formula.