If the side of an equilateral triangle decreased by 20%, its area is

Question

If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

Chethan92 · Answer

Let the side of an equilateral triangle be a.
Area is  \sqrt{3}/4*a^2 .
Now, the side becomes 0.8a,
New Area =  \sqrt{3}/4(0.8a)^2  =  \sqrt{3}/4*0.64a^2

% change =  \frac{New-Old}{Old} *100 = 0.36*100 = 36%

A is the answer.

Archit3110 · Answer

let side be 10 and later 20% less 80
area with side 10 = 25 sqrt 3 and with side 8- 16 sqrt 3
so % decrease = 9 /25
36 %
IMO A

KanishkM · Answer

Let the side be 100, Initial Area = 2500 root3

After reduction each side became 80
New area = 1600 root3

Difference between areas = 900 root3

900/2500 *100

Area was decreased by 36%

IMO A

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ScottTargetTestPrep · Answer

We use the formula for the area of an equilateral triangle: (a^2 x √3)/4, where a is the side. If the initial side is 10, then the original area is (10^2 x √3)/4 = 100√3/4 = 25√3.

Since the side decreased by 20%, the new side is 8, and the new area is (8^2 x √3)/4 = 64√3/4 = 16√3.

We use the percent change formula: (New - Old)/Old x 100. The percent change is:

(16√3 - 25√3)/25√3 x 100

-9√3/25√3 x 100

-9/25 x 100 = -36%, which is a 36% decrease.

Alternate solution:

We can use the fact that if a side of a regular polygon (equilateral triangle, square, regular pentagon, etc.) is increased or decreased such that the side’s new length is n times its original length, then the new area of the polygon is n^2 times its original area.

Since here the side of an equilateral triangle decreased by 20%, the side’s new length is 0.8 times its old length and thus the new area of the equilateral triangle is 0.8^2 = 0.64 times its original area, i.e., 64% of its original area. We see that this is a 36% decrease.

Answer: A

VoltAmpere · Answer

We can use the relationship between similar figures:
x1: original length of side
a1: original area
x2: new length
a2: new area

(x2/x1)^2=a2/a1
x2=x1-0.2x1=0.8x1
(0.8x1/x1)^2=a2/a1
0.8^2=a2/a1
a2=0.64a1
new area is 64% of original area,
therefore area decreased by 100%-64%=36%

CORRECT ANSWER: A

MathRevolution · Answer

If the side length is increased or decreased in an equilateral triangle, then  a^2  will change.

Let the old side be 10. Then  a^2 = 10 ^2 = 100

After 20 % decrease, new side becomes  10 * \frac{80 }{ 100} = 8 . Then  a^2 = 8 ^2 = 64

Percent change:  \frac{(64 - 100)}{100} * 100 = -36%

Answer A

chacinluis · Answer

Let
L= area of larger triangle
S= area of smaller triangle

The large and small triangle are similar.

Scale Factor= 1/0.8=5/4

Fact: Given two similar triangles. The area of the larger triangle is the square of the scale factor multiplied with smaller area.

Therefore 
L=(5/4)^2*S

Percent Change
(S-L)/L =   / (5/4)^2*S =   / (5/4)^2 =   / (25/16) = (-9/16) / (25/16) = -9/25 = -36/100 =-0.36

Final Answer: A

If the side of an equilateral triangle decreased by 20%, its area is

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If the side of an equilateral triangle decreased by 20%, its area is

Prep Toolkit

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