The hypotenuse of a right angled triangle is $ 5 \mathrm{~cm} $ and the other two sides differ by $ 1 \mathrm{~cm} $. Find the other two sided of the triangle.

Given:

The hypotenuse of a right angled triangle is \( 5 \mathrm{~cm} \) and the other two sides differ by \( 1 \mathrm{~cm} \).

To do:

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

Solution:

Let the other two sides of the triangle be $x$ cm and $x-1$ cm.
 Therefore, using Pythagoras theorem, we get,

$x^2+(x-1)^2=5^2$

$x^2+x^2+1-2x=25$

$2x^2-2x+1-25=0$

$2x^2-2x-24=0$

$x^2-x-12=0$

$x^2-4x+3x-12=0$

$x(x-4)+3(x-4)=0$

$(x+3)(x-4)=0$

$x=4$ or $x=-3$ which is not possible because the length cannot be negative.

$\Rightarrow x=4$ 

$\Rightarrow x-1=4-1=3$ 

The other two sides of the triangle are $3\ cm$ and $4\ cm$.

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Updated on: 10-Oct-2022

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