Question

The length of one of the legs of a right triangle exceeds the length of the other leg by 10 cm but is smaller than that of the hypotenuse by 10 cm. Find the length of the hypotenuse of the triangle.

Answer 1

Let the length of the smallest leg be $x$. Then the length of the other leg is $x+10$ and the length of the hypotenuse is $x+20$. using the Pythagorean theorem, we get,

$(x+20{)}^2=x^2+(x+10{)}^2$

$⟹x^2-20x-300=0$

solving this quadratic equation, we get, $x=30$. We discard the negative value.

Thus the length of the hypotenuse is $50$