Question

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

Answer 1

Let x be the length of the third side.

For a right-angled triangle, a^2+b^2=c^2

If p and q are the hypotenuse and length of the other side, then

x^2 + q^2 = p^2

thus, x^2 = p^2 - q^2

or x^2 = (p+q)*(p-q). Since a^2-b^2 = (a+b)*(a-b)

but it is given that p-q = 1. Substituting p-q=1 in the above equation, we get

x^2 = (p+q)*1 = (p+q).

Thus, x = Sqrt(p+q)

Therefore, the third side is sqrt(p+q).

Answer 2

Answer:

The third side=√(p+q)