Question

The hypotenuse of a right angle triangle is $25$ cm. The difference between the lengths of the other two sides of the triangle is $5$ cm. Find the perimeter of the triangle.

Answer 1

Let $a$ and $b$ be the measure of two sides of the right triangle.

According to the given condition and applying Pythagoras theorem

$a-b=5a=b+5a^2+b^2=625{(b+5)}^2+b^2=6252b^2+25+10b=6252b^2+10b-600=0b^2+5b-300=0(b-15)(b+20)=0b=15orb=-20\Rightarrow a=20(\text{since measure of side cannot be negative)}$
Hence, the sides of the triangle are $15,20$ and $25$.
Perimeter $=15+20+25=60$ cm.