Question

Hypotenuse of a right triangle is $25cm$ and out of the remaining two sides, one is longer than the other by $5cm$. Find the lengths of the other two sides.

• A. $10$cm and $20$ cm
• B. $15$cm and $20$ cm
• C. $25$cm and $20$ cm
• D. $5$cm and $20$ cm

Answer 1

The correct option is B $15$cm and $20$ cm

Let one side be $xcm$. Then the other side will be $(x+5)cm$. Therefore, from Pythagoras theorem
$x^2+{(x+5)}^2={25}^2$
$\Rightarrow x^2+x^2+10x+25=625$
$\Rightarrow x^2+5x-300=0\Rightarrow x^2+20x-15x-300=0$
$\Rightarrow x(x+20)-15(x+20)=0$
$\Rightarrow (x-15)(x+20)=0\Rightarrow x=15orx=-20$
Rejecting $x=-20$, we have length of one side $=15cm$ and that of the other side $=(15+5)cm=20cm$