Question

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

Answer 1

Hypotenuse = p cm
One side = q cm
Let the length of the third side be x cm.
Using Pythagoras theorem,
x² = p² - q² = (p + q)(p - q)
= (p ++ q) x 1   ...[∵ p - q = 1, given]
= p + q
∴ x = `sqrt("p" + "q")`
Thus, the length of the third side of the triangle is `sqrt("p" + "q")"cm"`.