Question

The area of the equilateral triangle is $20\sqrt{3}c{m}^2$ whose each side is$8cm$. Write True or False and justify your answer.

• A. True
• B. False

Answer 1

The correct option is B False

Area of an equilateral triangle of side $a=\frac{\sqrt{3}}{4}{a}^2$

According to the given details

Area of a triangle $=20\sqrt{3}c{m}^2$

$$\begin{gathered} \Rightarrow \frac{\sqrt{3}}{4}{a}^2=20\sqrt{3} \\ \Rightarrow a^2=20\times 4 \\ \Rightarrow a^2=80 \\ \Rightarrow a=4\sqrt{5}cm \end{gathered}$$

Thus, the length of its each side is $4\sqrt{5}cm$which is not equal to $8cm$

Hence, the given statement is “FALSE”