# The hypotenuse of a right triangle is 25 cm.

Question:

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

Solution:

Let the length of one side of right triangle be $=x \mathrm{~cm}$ then other side be $=(x+5) \mathrm{cm}$

And given that hypotenuse $=25 \mathrm{~cm}$

As we know that by Pythagoras theorem,

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

$x^{2}+x^{2}+10 x+25=625$

$2 x^{2}+10 x+25-625=0$

$2 x^{2}+10 x-600=0$

$x^{2}+5 x-300=0$

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

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

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

So, either

$(x-15)=0$

$x=15$

Or

$(x+20)=0$

$x=-20$

But the side of right triangle can never be negative

Therefore, when $x=15$ then

$x+5=15+5$

$=20$

Hence, length of one side of right triangle be $=15 \mathrm{~cm}$ then other side be $=20 \mathrm{~cm}$