Question

Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m2.

Answer 1

Let a = 51m, b = 37m, c = 20m

s = (a + b + c)/2 = (51 + 37 + 20)/2 = 108/2 = 54 m

∴ Area of triangular ground = root under(√s(s - a)(s - b)(s - c))

= root under√54(54 - 51)(54 - 37)(54 - 20)

= root under (√54 x 3 x 17 x 34) = 306 m2

Cost of levelling the ground = Rs 3 x 306 = Rs 918

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Answer 2

Given :

• Sides of triangle = 51 m , 37 m , 20 m

To Find :

• Cost of levelling the ground

Solution :

First we have to find area of triangle.

Semi-perimeter of triangle

$\implies\boxed{\boxed{\sf s = \frac{a + b + c}{2}}} \\ \\ \sf\implies s = \frac{51 + 37 + 20}{2} \\ \\\sf\implies s = \frac{108}{2} \\ \\\sf\implies s = 54$

Area of triangle by Heron's formula

$\large\implies\boxed{\boxed{\sf Area = \sqrt{s(s - a)(s - b)(s - c)}}} \\ \\\sf\implies \sqrt{54(54 - 51)(54 - 37)(54 - 20)} \\ \\\sf\implies \sqrt{54 \times 3 \times 17 \times 34} \\ \\ \sf\implies \sqrt{3 \times 3 \times 3 \times 2 \times 3 \times 17 \times 17 \times 2} \\ \\ \sf\implies3 \times 3 \times 2 \times 17 \\ \\\sf\implies 306 \\ \\\large\implies\boxed {\boxed { \sf Area = 306 {cm}^{2} }}$

Cost of levelling the ground

$\sf\implies 1 \: {m}^{2} = 3 \\ \\ \sf\implies306 \: {m}^{2} = 306 \times 3 = 918$

Cost of levelling = Rs 918