Expert: Scott A Wilson - 1/16/2012

Question
Area of a rectangle is 50m2
Diagonal is 10m
Perimeter?

Answer
All measurements are in meters, so I'll just use numbers.
The area is 50 and the diagonal is 10.

If the sides are A and B, then AB = 50 and A²+B²=10².
Using AB = 50, divide both side by A, giving B = 50/A.

Putting this in A² + 50²/A² = 10².
Letting C = A² gives C + 2500/C = 100.
Multiplying by C gives C² + 2500 = 100C.

Putting in the proper form of a quadratice gives C² - 100C + 2500 = 0.
That factors to (C-50)² = 0, so C = 50.

Since C = A², A = √50 = 5√2.
That make B = 50/(5√2) = 5√2, so it is a square.

The diagonal is √(50 + 50) = √100 = 10, so that checks out as well.