The perimeter and the area of a right-angled triangle are 36 cm and 54 square cm respectively. What is the length of the hypotenuse?

Explanation

Perimeter p+b+h = 36. Area \frac{1}{2}pb = 54 \implies pb=108. Using p^2+b^2=h^2, we write (p+b)^2 - 2pb = h^2 \implies (36-h)^2 - 216 = h^2. Expanding gives 1296 - 72h = 216 \implies 72h = 1080 \implies h=15 cm.

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