Question

The cost of levelling a ground in the form of a triangle having the sides $51$ m, $37m,$ and $20m$ at the rate of Rs.$3$ per $m^2$ is Rs. $918$. State whether the statement is true or false and justify your answer.

• A. True
• B. False

Answer 1

The correct option is A True

Step 1: Calculate the area of triangle using Heron's formula

According to Heron's formula Area of a triangle having side lengths as ‘a’, ‘b’, ‘c’ is given as:

$Area=\sqrt{s(s-a)(s-b)(s-c)}$ where, ‘s’ is the semi perimeter.

Find the semi perimeter

$$\begin{gathered} s=\frac{a+b+c}{2} \\ =\frac{51+37+20}{2} \\ =\frac{108}{2} \\ =54m \end{gathered}$$

Now find the area of the pyramid

$$\begin{gathered} A=\sqrt{54(54-51)(54-37)(54-20)} \\ =\sqrt{54\left(3\right)\left(17\right)\left(34\right)} \\ =\sqrt{2\times 3\times 3\times 3\times 3\times 17\times 2\times 17} \\ =2\times 3\times 3\times 17 \\ =306m^2 \end{gathered}$$

Step 2: Finding the cost of levelling

Cost of levelling = Rate multiplied by Area

Cost of levelling $$\begin{gathered} =3\times 306 \\ =918Rs. \end{gathered}$$

Since the cost calculated is same as given in the question.

Hence, the given statement is true.