Question

3)How much area of a triangle will increase if its each side is doubled. Calculate the percentage increase   

200%

300%

400%

500%

pls give me the solution. l know the answer is option 2​

Answer 1

Solution:

First, the sides (perimeter) of the triangle is P = a + b + c

Then the semi perimeter would be
P’ = (a + b + c)/2

Second, when each side is doubled, the new sides are P = 2a + 2b + 2c

Then the semi perimeter is doubled would be P’ = (2a + 2b + 2c)/2

Simplify
[2(a + b + c)/2] = 2P’ or 2s (sides)


The area of triangle is
A = √s(s - a) (s - b ) (s - с)

The area of triangle when it is doubled

A’ = √2s (2s - 2a) (2s - 2b) (2s - 2c)

Simplify, it would be

= √2 x 2 x 2 x 2 x s(s - a) (s - b) (s - c)

Then

= 4√s (s - a) (s - b) (s - c)

Next, let change to percent %

Area = (A’ - A)/A x 100

= [4√s (s - a) (s - b) (s - c)] - [√s (s - a) (s - b) (s - c)] / [√s (s - a) (s - b) (s - c)] x 100

= (4 - 1)/1 x 100 = 300%

Hope this will be helpful to you.