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.

Given:

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.

To do:

We have to find the lengths of the other two sides.

Solution:

Let the length of one of the other two sides be $x$ cm.

This implies, the length of the third side$=x+5$ cm.

We know that,

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. (Pythagoras theorem)

Therefore,

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

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

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

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

$2(x^2+5x-300)=0$

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

Solving for $x$ by factorization method, we get,

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

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

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

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

$x=-20$ or $x=15$

Length cannot be negative. Therefore, the value of $x$ is $15$.

$x+5=15+5=20$

The lengths of the other two sides are $15$ cm and $20$ cm.

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Updated on: 10-Oct-2022

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