Question

Find percentage increase in area of a triangle if its each side is doubled

Answer 1

Hey !!

Thanks for the question !!

For this case, let me consider an equilateral triangle.

Properties of Equilateral Triangle :

1. It has equal sides

2. It has equal angles ( 60° )

3. Perimeter = 3 * Side 

4. Area = Side * √ 3 / 4

Given : Equilateral triangle with side " a "

To find : Area increase 

Proof : 

Area of original triangle before increase = a √ 3 / 4 units

Now Side is increased by twice the original length. So new side is 2a

So new area = 2a √ 3 / 4 
Therefore Percentage increase = New area - Old area / Old area * 100

=> 2a √ 3 - a √ 3 / 4 / a √ 3 / 4 * 100

4 gets cancelled. Hence we get,

=> a √ 3 / a √ 3 * 100

=> 1 * 100 = 100 %

Hence the area has remained same even after increase in area also.

Hope my answer helped !!