Math CentralQuandaries & Queries


Question from steven, a student:

the perimeter of a right triangle is 20 cm. its area is 15 sq cm. find its hypotenuse.


Let the legs of the triangle have lengths x and y cm and the hypotenuse have length h cm.

The perimeter is 20 cm

x + y + h = 20.

The area is 15 sq cm

xy/2 = 15.

Hypotenuse tell us that

x2 + y2 = h2.


y = 30/x and h = Sqrt(x2 + y2) = Sqrt(x2 + (30/x)2)

Substitution into the first equation gives

Sqrt(x4 + 900) = 20x - x2 - 30.

Square both sides and simplify. The resulting equation is a quadratic which you can factor to find x.


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