Question

The sides of a triangular field are in the ratio $5:3:4$ and its perimeter is $180m$. Find:
(i) its area
(ii) altitude of the triangle corresponding to its largest side
(iii) the cost of levelling the field at the rate of Rs. $10$ per square metre

Answer 1

Let the side be $5x,3x$ and $4x$

$5x+3x+4x=180$

$12x=180$

$x=15$

Sides $=75,45,60$

(i) S $=\frac{75+45+60}{2}=\frac{180}{2}=90$

Area $=\sqrt{90(90-75)(90-45)(90-60)}$
$=\sqrt{90\times 15\times 45\times 30}$

$=1350m^2$

(ii) $\frac{1}{2}\times 75\times a=1350$ [Ref. image]
$a=36m$

(iii) Total cost $=10\times Area$

$=10\times 1350$

$=Rs.13500$