Question

The area of an equilateral triangle is 25√3 . Determine the lengths of its sides and its altitude.

Answer 1

The formula for determining the area of a triangle is expressed as

Area = 1/2 x base x height

The formula for determining the area of an equilateral triangle is expressed as

`\text{Area = }\frac{a^2\sqrt[]{3}^{}}{4}`

where a is the length of each side of the triange.

Given that the area of the triangle is 25√3, we have

`\begin{gathered} 25\sqrt[]{3}\text{ =}\frac{a^2\sqrt[]{3}^{}}{4} \\ a^2\sqrt[]{3}\text{ = 4 x 25}\sqrt[]{3} \\ a^2\text{ = }\frac{100\sqrt[]{3}}{\sqrt[]{3}} \\ a^2\text{ = 100} \\ a\text{ = }\sqrt[]{100} \\ a\text{ = 10} \end{gathered}`

The formula for determining the altitude is

`\begin{gathered} h\text{ = }\frac{a\sqrt[]{3}}{2} \\ h\text{ = }\frac{10\sqrt[]{3}}{2} \\ h\text{ = 5}\sqrt[]{3} \end{gathered}`

The length of each side is 10

The altitude is 5root3