Answer
The lengths of the sides of the right triangle are,
hypotenuse = 25 cm
longer leg = 20 cm
shorter leg = 15 cm
Work Step by Step
Let $x$ cm be the length of the hypotenuse.
Since the hypotenuse is 10 centimeters longer than the shorter leg, the shorter leg = $x - 10$,
and the hypotenuse is 5 centimeters longer than the longer leg, the longer leg = $x - 5$
By Pythagoras Theorem,
$(x - 10)^2 + (x - 5)^2 = x^2$
$x^2 - 20x + 100 + x^2 - 10x + 25 - x^2 = 0$
$x^2 - 30x + 125 = 0$
$(x - 25)(x - 5) = 0$
$x = 25$ or $x = 5$ (rejected)
Therefore, the lengths of the sides of the right triangle are,
hypotenuse = 25 cm
longer leg = 25 - 5 = 20 cm
shorter leg = 25 - 10 = 15 cm
