Question

The sides of a triangular field are in the ratio $5:3:4$ and its perimeter is $180$ m, then find the cost of levelling the field at the rate of Rs. $10$ per square meter.

Answer 1

Let the sides of the triangular field be $5a,3a,4a$.

Perimeter of the triangle $=$ Sum of all sides $=5a+3a+4a=12a$

Given, perimeter of the triangular fied $=180$ m

$⟹12a=180$ m

$a=15$ m

So, the sides of the triangular field are $5a=75$ m, $3a=45$ m, $4a=60$ m.

Area of triangle with sides $a,b,c$ and $s$ $=\frac{a+b+c}{2}$ is $\sqrt{s(s-a)(s-b)(s-c)}$.

For the triangular field with sides $75$ m, $45$ m and $60$ m, $s=\frac{75+45+60}{2}=90$ m

Area of the triangular field with sides $75$ m, $45$ m and $60$ m $=\sqrt{90(90-75)(90-45)(90-60)}$

$=\sqrt{90\times 15\times 45\times 30}$

$=\sqrt{15\times 6\times 15\times 15\times 3\times 15\times 2}$

$=15\times 15\times 6$

$=1350m^2$

Cost of levelling the field at the rate of Rs.$10$ per square metre $=1350\times 10=$ Rs. $13500$.