Question

The perimeter of right-angled triangle is 60 cm. And it's hypotenuse is 25 cm. Then find the area of the triangle.

Answer 1

It is Right angled traingle and

It's hypotenuse is 25 cm

Now, perimeter$=60cm$

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

By pythegoras theorem, we have,

$A{B}^2+B{C}^2=A{C}^2$

Now, ${25}^2=x^2+(35+x{)}^2$
$625=x^2+1225+x^2+70x$ $[\because (a+b{)}^2=a^2+b^2+2ab]$
$\Rightarrow 2x^2+70x+600=0$

$\Rightarrow x^2-35x+600=0$

Now finding the value of $x$,

So, $x^2-20x-15x+600\Rightarrow x(x-20)-15(x-20)\Rightarrow x=20Orx=15$

Case 1:

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

Area $=\frac{1}{2}\times BC\times AB=\frac{1}{2}\times 20\times 15=150c{m}^2$

Case 2:

When $x=15$ then $AB=35-x=20,BC=15cm$

Area$=\frac{1}{2}\times 15\times 20=150c{m}^2$