Find its dimensions and perimeter

Question

The area of a rectangle is 24, and it's diagonal is √5.

Longer side?

Shorter side?

Perimeter?

Answer 1

The diagonal is the hypotenuse of a right triangle with the two legs of x and 24/x.

 

(√5)² = x² + (24/x)²           square terms

5 = x² + 576/x²                  multiply both sides by x²

5x² = x⁴ + 576                   subtract 5x² form both sides

0 = x⁴ - 5x² + 576

 

This equation does not have any real roots. Please check your numbers.