Question

The sides of a triangular field are $20m$, $37m$ and $51m$. Find the number of flower beds that can be prepared if each bed measures $(2\times 3)m^2$ .

Answer 1

Step 1: Find the area of the triangular field

To find the area of the triangle, we will use 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.

So, the semi-perimeter will be,

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

Now, the area of the triangular field will be,

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

Step 2: Find the area of the flower bed

Since it is given that the bed measures are $(2\times 3)m^2$.

So the area of each flower bed is $6m^2$.

Step 3: Find the number of flower beds

The number of flower beds can be calculated as: $\frac{areaoftriangularfield}{areaofeachflowerbed}$

Thus, the number of flower beds will be,$=\frac{306}{6}$

$=51$

Hence, the number of flower beds in the triangular field will be $51$.