Question

Find the cost of laying grass in a triangular field of sides $50\mathrm{m}$, $65\mathrm{m}$ and $65\mathrm{m}$ at the rate of $₹7$ per ${\mathrm{m}}^2$

Answer 1

Step 1: Find area of triangular field

Given, lengths of the three sides of the triangular field are $50\mathrm{m}$, $65\mathrm{m}$ and $65\mathrm{m}$

To find area of a triangle when lengths of the three sides are given, we can use heron's formula which is given as,

$\mathrm{area}=\sqrt{s(s-a)(s-b)(s-c)}$

where, $a$, $b$ and $c$ are the three sides of the triangle and $s$ is the semi-perimeter given as $s=\frac{a+b+c}{2}$

The semi-perimeter of the park is,

$$\begin{gathered} s=\frac{a+b+c}{2} \\ =\frac{50+65+65}{2} \\ =90 \end{gathered}$$

Thus ,the area of the triangular field is,

$$\begin{gathered} \mathrm{area}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{90(90-50)(90-65)(90-65)} \\ =\sqrt{2250000} \\ =1500\mathrm{m} \end{gathered}$$

Step 2: Calculate the cost of laying grass

Rate of laying grass per ${\mathrm{m}}^2$ is$₹7$

Cost of laying grass $=\mathrm{area}\times \mathrm{cost}$

$$\begin{gathered} =1500\times 7 \\ =₹10,500 \end{gathered}$$

Therefore, the cost of laying grass in the triangular field is $₹10,500$.