The hypotenuse of a right triangle is 25 cm. The other two sides are such that one is 5 cm longer.

Solution:

(b) 15 cm, 20 cm

It is given that the length of hypotenuse is 25 cm.

Let the other two sides be $x \mathrm{~cm}$ and $(x-5) \mathrm{cm}$.

Applying Pythagoras theorem, we get:

$25^{2}=x^{2}+(x-5)^{2}$

$\Rightarrow 625=x^{2}+x^{2}+25-10 x$

$\Rightarrow 2 x^{2}-10 x-600=0$

$\Rightarrow x^{2}-5 x-300=0$

$\Rightarrow x^{2}-20 x+15 x-300=0$

$\Rightarrow x(x-20)+15(x-20)=0$

$\Rightarrow(x-20)(x+15)=0$

$\Rightarrow x-20=0$ or $x+15=0$

 

$\Rightarrow x=20$ or $x=-15$

Side of a triangle cannot be negative.

Therefore, $x=20 \mathrm{~cm}$

Now,

$x-5=20-5=15 \mathrm{~cm}$