Question

The hypotenuse of a right-angled triangle is $25cm$. The other two sides are such that one side is $5cm$ longer than the other side. Their lengths, in $cm$, are:

• A. $5cm,10cm$
• B. $10cm,15cm$
• C. $15cm,20cm$
• D. $12cm,17cm$

Answer 1

Answer: (C)

$15cm,20cm$

Let the sides be $x$ and $x+5$
Using Pythagoras Theorem
$x^2+(x+5{)}^2={25}^2$
$\Rightarrow x^2+x^2+25+10x=625$
$\Rightarrow 2x^2+10x-600=0$
$\Rightarrow x^2+5x-300=0$
Solving it we get $x=15$
So, sides are $15cm$ and $20cm$