A right triangle has a hypotenuse length of cm and a perimeter of cm. Find the lengths of the other two sides.
Denote the other two sides of the triangle using and . If the perimeter of the triangle is cm, then
which simplifies to
As the triangle is right-angled, it satisfies Pythagoras' theorem. Therefore,
This pair of equations can be solved by substitution. Rearranging the first order equation gives
Substituting into the second order equation gives
Dividing by 2 gives
This equation can be solved by factorisation.
Now substitute each -value into the first order equation to find .
The lengths of the two sides are cm and cm.