A right-angled triangle has shorter side lengths exactly c^2-b^2 and 2bc units respectively, where b and c are positive real numbers such that cc is greater than b. Find an exact expression for the length of the hypotenuse (in appropriate units).

hypotenuse =

Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side () of the right triangle, .i.e.:

In this question:

=

2bc

Substituing and taking square root to find hypotenuse:

Calculating:

= , then:

Hypotenuse for the right-angled triangle is units

or