 # Find the cost of laying grass in `
Question:

Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs. 7 per m2.
Thinking Process

(i) First, determine the semi-perimeter s by using formula $s=\frac{a+b+c}{2}$ and then

determine the area of a triangle by using Heron's formula $\sqrt{s(s-a)(s-b)(s-c)}$

(ii) Cost of laying grass = Area of field $\left(\right.$ in $\left.m^{2}\right) \times\left(\right.$ Cost of laying grass in $\left.1 m^{2}\right)$

Solution:

Since, $A B C$ is a triangular field of sides

$A B=a=50 m, B C=b=65 m$ and $C A=c=65 m$. $\therefore$ Semi-perimeter of triangular field,

$s=\frac{a+b+c}{2}=\frac{50+65+65}{2}=\frac{180}{2}$

$s=90 \mathrm{~m}$

$\therefore$ Area of a triangular field

$=\sqrt{s(s-a)(s-b)(s-c)}$                  [by Heron' formula]

$=\sqrt{90(90-50)(90-65)(90-65)}$

$=\sqrt{90 \times 40 \times 25 \times 25}$

$=3 \times 2 \times 10 \times 25$

$=6 \times 250=1500 \mathrm{~m}^{2}$

$\because$ Cost of laying grass per $1 \mathrm{~m}^{2}=₹ 7$

$\therefore$ Cost of laying grass per $1500 \mathrm{~m}^{2}=7 \times 1500=₹ 10500$

Hence, the cost of laying grass in a triangular field is ₹10500.