Question

The perimeter of a right triangle is $24cm$. If its hypotenuse is $10cm$, find its area.

Answer 1

Perimeter of the triangle $=24$ cm

$AB+BC+AC=24$

$a+b+10=24$

$a+b=14$ ............ (1)

From Pythagoras theorem,

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

$a^2+b^2={10}^2$

$a^2+b^2=100$ ........... (2)

Now,

$(a+b{)}^2=a^2+b^2+2ab$

From (1) and (2),

$(14{)}^2=100+2ab$

$\Rightarrow 2ab=196-100$

$2ab=96$

$ab=48$

Area of the triangle $=\frac{1}{2}\times base\times height$

$=\frac{1}{2}ab$

$=\frac{48}{2}$

$=24$ $c{m}^2$