If each side of a triangle is increased by 200%, by what percent will

Question

If each side of a triangle is increased by 200%, by what percent will its area increase?

A. 200%
B. 300%
C. 400%
D. 800%
E. 900%

Are You Up For the Challenge: 700 Level Questions

If each side of a triangle is increased by 200%, what is the change in the area of the triangle?

CrackverbalGMAT · Answer

We can do this by similarity of triangles.

If one of the sides of the original triangle is x, then an increase by 200% will make the side of the new triangle as 3a.

Therefore the ratio of sides = 1/3

From similarity, the ratio of areas = square of the ratio of sides =  (\frac{1}{3})^2 = \frac{1}{9}

Let the areas be y and 9y

Therefore % Increase =  \frac{Difference}{Smaller \space Value} * 100 = \frac{9y - y}{y} * 100  = 800%

Option D

Arun Kumar

GMATinsight · Answer

Increasing x by 200%  = x+(\frac{200}{100})*x = 3x

i.e. each side has been three times the originial length

Area of triangle  = (\frac{1}{2})*Base*Height  = P (Let)

NEW  Area of triangle  = (\frac{1}{2})*3*Base*3*Height = (\frac{1}{2})*Base*Height*9  = 9P

i.e. % change in ARea  = \frac{9P-P}{P}*100 = 800%

Answer: Option D

Abhishek009 · Answer

200 + 200 + \frac{200*200}{100} = 400 + 400 = 800 , Answer must be (D)

Archit3110 · Answer

let ∆ be 3:4:5
area is 1/2 * 3*4 ; 6
with 200 % increase side become
9:12:15
area is 1/2 * 9* 12 ; 54
%∆=54-6/6 ; 48/8 ; 800%
option D

BrentGMATPrepNow · Answer

Another approach is to test a certain case.

ASIDE: Keep in mind that increasing a number by 200% is the SAME as multiplying that number by 3.

So, if the original triangle has measurements   1-1-√2  , then the enlarged triangle has measurements   3-3-3√2  
 https://i.imgur.com/iMvPjE9.png 
Area of original triangle = (base)(height)/2 =   (1)(1)  /2 =   0.5  
Area of enlarged triangle = (base)(height)/2 =   (3)(3)  /2 =   4.5

Percent increase = (100)(new - old)/old = (100)(  4.5   -   0.5  )/  0.5  
= (100)(4)/(0.5) 
= 400/0.5 
= 800%

Answer: D

If each side of a triangle is increased by 200%, by what percent will

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If each side of a triangle is increased by 200%, by what percent will

Prep Toolkit

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