What is the diagonal length of a rectangle whose area is 212.268 square cm with a perimeter of 61.18 cm showing all work with answer?

Answer 1

Let the dimensions of the rectangle be x and y and divide its perimeter by 2:-

So: x+y = 30.59 => y = 30.59 -x

Area: xy = 212.268 => x(30.59 -x) = 212.268

It follows that: 30.59x - xsquared -212.268 = 0

Solving the quadratic equation: x = 19.95 or x = 10.64

By substitution: x = 19.95 and y = 10.64

Using Pythagoras: 19.95squared+10.64squated = 511.2121

The square root of 511.2121 is 22.61 cm which is the diagonal length