Question

The sides of a triangular plot are 26 m, 28 m, and 30 m. what is the cost of levelling the plot at the rate of Rs.15/m²?
1. Rs.5040
2. Rs.4960
3. Rs.4080
4. Rs.3520

Answer 1

Correct Answer - Option 1 : Rs.5040

Given:

Sides of a triangle = 26 m, 28 m and 30 m

Cost of levelling = Rs. 15/m²

Formula used:

Area of a triangle = \(√{s(s \ - \ a)(s \ - \ b)(s \ - \ c)}\)

Semiperimeter(s) = \(\dfrac{a \ + \ b \ + \ c}{2}\)

Calculation:

The semiperimeter of the triangle is

\(\dfrac{30 \ + \ 28 \ + \ 26}{2}\) = 42 m

Area of the triangle

= \(\sqrt{42(42 \ - \ 30)(42 \ - \ 28)(42 \ - \ 26)}\)

⇒ \(\sqrt{42\ × \ 12\ × \ 14\ × 16}\) = √112896 = 336 m²

The price of levelling is

336 × 15 = Rs. 5040

∴ The cost of levelling the plot is Rs. 5040.