Question

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

Answer 1

Step 1 : Find the area of triangular field

Given : Sides of triangular field are $50$ m, $65$ m, $65$ m

As, two sides of the triangle are equal.
Thus, the given triangle is an isosceles triangle.

Here, $\text{base}\left(a\right)=50m,\text{equal sides}\left(b\right)=65m$

$\therefore \text{Area of isosceles triangle}=\frac{a}{4}\sqrt{4b^2-a^2}$

$=\frac{50}{4}\sqrt{4(65{)}^2-(50{)}^2}$

$=\frac{50}{4}\sqrt{16900-2500}$

$=\frac{25}{2}\sqrt{14400}$

$=\frac{25}{2}\sqrt{12\times 12\times 10\times 10}$

$=\frac{25}{2}\times 120$

$=1500$

Thus, area of the traingular field is $1500m^2$

Step 2 : Find the total cost

Cost of $1m^2=\text{Rs}7$

Total cost of $1500m^2=\text{Rs}1500\times 7$

$=\text{Rs}10500$

Hence, the cost of lying grass in a triangular field is $\text{Rs}10500$