Question

If the sides of a triangular field measure $51m$, $37m$ and $20m$, then the cost of leveling it at $Rs.5$ per $m^2$ is $Rs.1540$.

• A. True
• B. False

Answer 1

The correct option is B False

Step 1: Find the area of the triangle:

Triangle: A three-sided polygon that has three vertices, angles, and sides.

Since it is given that the sides of the triangle are $a=51m,b=37m,c=20m$.

Using Heron's formula,

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

Where $s=\frac{a+b+c}{2}$ and $a,b,c$ are the sides of the triangle.

Now, the semi-perimeter will be,

$$\begin{gathered} s=\frac{51+37+20}{2} \\ \Rightarrow s=\frac{108}{2} \\ \Rightarrow s=54cm \end{gathered}$$

Hence, the area of the triangle will be,

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

Step 2: Find the cost of leveling

Since it is given that the cost of leveling is $Rs.5$ per $m^2$ .

So, the total cost of leveling will be,$=Area\times Costofleveling$

$$\begin{gathered} =306\times 5 \\ =Rs.1530 \end{gathered}$$

Hence, the given statement is False.