Question

The cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of ₹7 per $m^2$ is ___ .

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

Answer 1

The correct option is C

₹ 10,500

Let the sides of the given triangular field be:
a = 50 m
b = 65 m
c = 65 m
Given that laying grass costs ₹ 7 per $m^2$.
We need to find the area of this triangular field, using Hheron's formula.
$\text{Semi-perimeter},s=\frac{50+65+65}{2}=\frac{180}{2}=90m$

Area of triangular field

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

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

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

$=\sqrt{10\times 3\times 3\times 10\times 2\times 2\times 25\times 25}$

$=10\times 3\times 2\times 25=1500m^2$

Cost of laying grass $=7\times 1500$

$=₹10,500$