Question

Find the cost of laying grass in a triangular field of sides 50 m, 65m, 65m, at the rate of ₹7 per m square
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Answer 1

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$\text{\large\underline{\purple{Given:-}}}$

Sides of triangular field = 50m, 65m and 65m

To find:-

The cost of lying grass at the rate of 7 Rs per m²

$\text{\large\underline{\pink{Solution:-}}}$

★ Using heron's Formula:-

Firstly we need to find semi - perimeter (S)

★Perimeter (P) of ∆ = (a + b + c)

= (50m + 65m + 65m)

= 180m

Therefore, Semi - perimeter:-

$\implies: Semi - perimeter = \sf \dfrac{Perimeter}{2}$

$\implies: Semi - perimeter = \cancel{ \dfrac{180}{2}}$

$\implies$ Semi perimeter = 90m

$\text{\large\underline{\purple{Therefore,}}}$

$Area = \sf \sqrt{S(S - a)(S - b)(S - c)}$

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

$⟹$ $\sf \sqrt{90 \times 40 \times 25 \times 25}$

$⟹$$\bold{ 60 × 5 × 5}$

$⟹$${\underline{\underline{\sf{\red{1500m^2}}}}}$

Now,

★ Cost of lying grass will be = Area × Rate

$⟹$$\bold{1500 × 7}$

$\implies:{\underline{\underline{\sf{\red{10500 Rs.}}}}}$

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Answer 2

Answer:

Cost = 10500

Explanation:

using Herons Formula

p = mean of a, b, c = 180/2 = 90

p = 90

p-a = 40

p-b= 25

p-c= 25

A= Root ( p . p-a. p-b. p-c)

A= ( 90.40.25.25)

A= 60x 25 = 1500

Cost= 7x1500