Question

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

Answer 1

Given:

Side 1 of triangular field = 50 m

Side 2 of triangular field = 65 m

Side 3 of triangular field = 65 m

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To Find:

Cost of laying grass in the triangular field at the rate of Rs. 7 per m²

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Solution:

First, we need to find the area of the triangular field in order to find the cost of laying grass. Since the formula Area =  $\sf \frac{1}{2}bh$ is not applicable here, we'll use Heron's Formula.

Heron's Formula → $\sf \sqrt{s(s-a)(s-b)(s-c)}$

Here,

s = Semi Perimeter

a = Side 1

b = Side 2

c = Side 3

So let's find the semi perimeter of the triangular field first.

⇒ s = (50 + 65 + 65) ÷ 2

⇒ s = 180 ÷ 2

⇒ s = 90 m

∴ Semi perimeter = 90 m.

Now, let's apply the Heron's Formula.

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

$\implies \sqrt{90(40)(25)(25)}$

$\implies \sqrt{(2 \times 5 \times 3\times 3) \times (2 \times 2 \times 2 \times 5)\times (5 \times 5) \times (5\times 5)}$

$\implies 2 \times 2 \times 3 \times 5\times 5 \times 5$

$\implies 1500 \ m^{2}$

∴ Area of Triangular Field = 1500 m²

Cost of laying grass at the rate of Rs. 7 per m² = 1500 × 7 = Rs. 10500

∴ The cost of laying grass in the triangular field at the rate of Rs. 7 per m² would be Rs. 10500.

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