Question

The sides of a triangular field are 33 m, 44 m and 55 m. the cost of levelling the field at the rate of Rs 1.20 per meter square is

Answer 1

The cost of leveling the field at a rate of Rs. 1.20 per meter square is Rs. 871.20

Heron's formula:

If $a$, $b$, $c$ be the sides of a triangle and $s$ be its semi-perimeter, then its area is given by

$\quad A=\sqrt{s(s-a)(s-b)(s-c)}$

Step-by-step explanation:

The given problem can be solved by three steps:

1. Finding the semi-perimeter of the triangle
2. Finding the area of the triangle using Heron's formula
3. Finding the cost of leveling the field

Check the steps below.

Step 1. Finding the semi-perimeter of the triangle

The sides of the triangle are $33$ m, $44$ m and $55$ m. Then its perimeter is

$\quad 2s=33+44+55$ m

$\Rightarrow 2s=132$ m

Then its semi-perimeter is

$\quad s=\dfrac{2s}{2}$

$\Rightarrow s=\dfrac{132}{2}$ m

$\Rightarrow \bold{s=66}$ m

Step 2. Finding the area of the triangle using Heron's formula

Using Heron's formula, we find the area of the given triangle,

$\quad A=\sqrt{66(66-33)(66-44)(66-55)}$ square meters

$\Rightarrow A=\sqrt{66\times 33\times 22\times 11}$ square meters

$\Rightarrow A=\sqrt{2\times 3\times 11\times 3\times 11\times 2\times 11\times 11}$ square meters

$\Rightarrow A=\sqrt{\underline{2\times 2}\times \underline{3\times 3}\times \underline{11\times 11}\times \underline{11\times 11}}$ square meters

$\Rightarrow A=2\times 3\times 11\times 11$ square meters

$\Rightarrow \bold{A=726}$ square meters

Step 3. Finding the cost of leveling the field

The cost of leveling the field can be found by multiplying the area of the field and the rate of leveling per square meter area.

So, the required cost

= Rs. (726 × 1.20)

= Rs. 871.20