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Mathematics

A right triangle has hypotenuse of length p cm and one side of length q cm. If p - q = 1, find the length of the third side of the triangle.

Pythagoras Theorem

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Answer

In a right angled triangle, using Pythagoras theorem,

Hypotenuse2 = (One side)2 + (Other side)2

⇒ p2 = q2 + (Another side)2

Let the third side be x.

⇒ x2 = p2 - q2

⇒ x2 = (p - q)(p + q)

⇒ x2 = 1 x (p + q)

⇒ x2 = p + q

⇒ x = p+q\sqrt{p + q}

Hence, the length of the third side of the triangle = p+q\sqrt{p + q} cm.

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