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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.