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# GEOMETRY V

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An equilateral triangle has sides of length 2 units. A second equilateral triangle is formed having sides that are 150% of the length of the sides of the first triangle. A third equilateral triangle is formed having sides that are 150% of the length of the sides of the second triangle. The process is continued until four equilateral triangles exist. What will be the percent increase in the perimeter from the first triangle to the fourth triangle? Express your answer to the nearest tenth.

Nov 17, 2019

#1
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The side lengths are  increased to  2 x 1.5 x 1.5 x 1.5 = 2 (1.5)3 = 6.75

original perimeter = 2 *3 = 6    new largest perimeter = 6.75 x 3 = 20.25

Per cent increase    20.25/6 x 100% = 337.5 %                    (now look at   1.53   this equals 3.375  )

Nov 17, 2019
#2
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I put 337.5% as my answer. It is incorrect.

Nov 17, 2019
#3
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An equilateral triangle has sides of length 2 units. A second equilateral triangle is formed having sides that are 150% of the length of the sides of the first triangle. A third equilateral triangle is formed having sides that are 150% of the length of the sides of the second triangle. The process is continued until four equilateral triangles exist. What will be the percent increase in the perimeter from the first triangle to the fourth triangle? Express your answer to the nearest tenth.

Doing this with percents confuses me.  Let's get rid of the % signs and say it as follows:

An equilateral triangle has sides of length 2 units. A second equilateral triangle is formed having sides that are 1.50 times the length of the sides of the first triangle, and so on.

The second triangle has sides 1.5 times the length of the first

And the third triangle has sides 1.5 times the length of the second

And the fourth triangle has sides 1.5 times the length of the third

So the fourth triangle has sides 1.5 x 1.5 x 1.5 times the length of the first

Do the multiplication, and the fourth triangle has sides 3.375 times the length of the first

Change the factor of 3.375 back to percent and the percent increase is 337.5 percent.  Stating that the first triangle's sides were 2 units long was a red herring.  The question asked for the percent increase

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Nov 17, 2019
#4
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It is incorrect though.

Nov 17, 2019
#5
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First triangle = 2 units
2nd triangle   =1.5 x 2 =3 units.
3rd triangle    =3 x 1.5 =4.5 units
4th triangle    =4.5 x 1.5 =6.75 units.
6.75 / 2 =3.375 - 1 x 100 =237.5% increase in the perimeter from the first to the 4th triangle.

Nov 17, 2019
#6
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Oh golly that's right.  It's the wording.  The fourth triangle is 3.375 times the first, therefore the INCREASE is 2.375.

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Guest Nov 17, 2019
#7
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Per cents are always kinda tricky

150% of 2  == 3    2nd side length

150% 0f 3  = 4.5

150% 0f 4.5 = 6.75

z% of 2 = 6.75

6.75/2 = 3.375           337.5%  OF 2      The INCREASE FROM 2    (6.75-2)/2 = 2.375 = 237.5 %

SO I think the wording is tricky, but the answer looked for is 237.5 %

Nov 17, 2019