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If a rectangle has width w and height h,

1) the area a = wh

2) the perimeter p = 2w + 2h

From 1), w=a/h

Substituting into 2)

p = 2a/h + 2h

Multiplying by h

pH = 2a + 2h2

Rearranging

2h2 - pH + 2a = 0 This is a quadratic equation in h.

Factorising, using the standard quadratic formula,

h = (p ± sqrt(p2 - 16a))/4

The two solutions to this will be the two dimensions.

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Q: How do you calculate dimensions of a rectangle using area and perimeter?
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