Question

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

• A. $10,200$
• B. $40,100$
• C. $10,500$
• D. $10,000$

Answer 1

The correct option is C

$10,500$

Step 1 Given data:
Sides of triangular field are $50m,65m$ and $65m$
Cost of laying grass is $Rs.7per{m}^2$.

Step 2 Heron's formula:
As we know, we can find the area of the triangle by using Heron's formula:
Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}\left(Heron\text{'}sformula\right)$ ,
Where $s=\frac{a+b+c}{2}$ and $a,b,c$ are the sides of the triangle.

Step 3 Find the area of triangle:
Sides of the given triangle, we have,

Let, $a=50m,b=65m,c=65m$
So, semi-perimeter of the triangle is,

$$\begin{gathered} s=\frac{50+65+65}{2} \\ =\frac{180}{2} \\ =90\mathrm{m} \end{gathered}$$

Now, area of triangular field will be

$$\begin{gathered} =\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{90(90-50)(90-65)(90-65)} \\ =\sqrt{90\times 40\times 25\times 25} \\ =\sqrt{2250000} \\ =1500m^2 \end{gathered}$$

Step 4 Cost of laying grass:
Cost of laying grass is $Rs.7per{m}^2$.

Cost of laying grass $=rate\times area=7\times 1500=Rs.10,500$

Hence, cost of laying grass is $Rs.10,500$
Therefore, option $\left(c\right)$ is the correct answer.