Question

The perimeter of a right triangle is $60cm$. Its hypotenuse is $25cm$. Find the area of the triangle.

Answer 1

Let $ABC$ be the given right angled triangle such that $base=BC=x$ cm and hypotenuse $AC=25cm$

Now, perimeter $=60cm$

$AB+BC+AC=60$
$AB+x+25=60$
$AB=35-x$

By Pythagoras theorem, we have
${AB}^2+{BC}^2={AC}^2$

$\Rightarrow {(35-x)}^2+x^2={25}^2\Rightarrow 2x^2-70x+600=0$

$\Rightarrow x^2-35x+300=0\Rightarrow x^2-20x-15x+300=0\Rightarrow (x-20)(x-15)=0\Rightarrow x=20orx=15$

If $x=20$, then $AB=35-x=15$ and $BC=x=20$

Area $=\frac{1}{2}(BC\times AB)=\frac{1}{2}(20\times 15)=150{cm}^2$

If $x=15$, then $AB=35-x=20$ and $BC=x=15$

Area $=\frac{1}{2}(BC\times AB)=\frac{1}{2}(15\times 20)=150{cm}^2$