Question

An equilateral triangle has the area of 36 √3 square units. What is the side length?

Answer 1

Step 1

Given;

`An\text{ equilateral triangle with area 36}\sqrt[]{3}unit^2`

Required; To find the side length.

Step 2

State the area(A) of an equilateral triangle.

`\begin{gathered} A=\frac{\sqrt[]{3}}{4}a^2 \\ \text{where a= side length} \end{gathered}`

Step 3

Find the side length

`\begin{gathered} A=36\sqrt[]{3}unit^2 \\ 36\sqrt[]{3}=\frac{\sqrt[]{3}}{4}a^2 \\ 144\sqrt[]{3}=\sqrt[]{3}a^2 \end{gathered}`
`\begin{gathered} \frac{\sqrt[]{3}a^2}{\sqrt[]{3}}=\frac{144\sqrt[]{3}}{\sqrt[]{3}} \\ a^2=144 \\ \sqrt[]{a^2}=\pm\sqrt[]{144} \\ a=\pm12\text{ units} \end{gathered}`

But, the side length cannot be negative, therefore, the side length of the equilateral triangle = 12 units