Question

The side of a right triangle containing right angle are $5cm$ and $(3x-1)cm$.If area of tiangle is $60c{m}^2$, find sides of triangle.

Answer 1

Area of traingle $=\frac{1}{2}\times$ (Product of sides containing right angle)

$\Rightarrow 60=\frac{1}{2}\times 5\times (3x-1)$

$\Rightarrow 24=3x-1$

$\Rightarrow 3x=25$

$\Rightarrow x=\frac{25}{3}cm$

By Pythagoras theorem

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

$=\frac{625}{9}+25=\frac{625+225}{9}=\frac{850}{9}$

$\Rightarrow AC=\frac{\sqrt{850}}{3}cm$