SOLUTION: Two similar triangles have perimeters of 18cm and 30 cm. Find the ratio of their areas.

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Question 452360: Two similar triangles have perimeters of 18cm and 30 cm. Find the ratio of their areas.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two similar triangles have perimeters of 18cm and 30 cm.
Find the ratio of their areas.
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Use two equilateral triangles
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Triangle 1, 6 cm on each side
find the height
h = sqrt%286%5E2-3%5E2%29
h = sqrt%2827%29
h = 3sqrt%283%29
Find area 1
A = .5*3sqrt%283%29*6
A = 3%2A3sqrt%283%29
A = 9sqrt%283%29 sq/cm
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Triangle 2, 10 cm on each side
find the height
h = sqrt%2810%5E2-5%5E2%29
h = sqrt%2875%29
h = 5sqrt%283%29
Find area 2
A = .5*5sqrt%283%29*10
A = 5%2A5sqrt%283%29
A = 25sqrt%283%29 sq/cm
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Find ratio of the two areas
%289sqrt%283%29%29%2F%2825sqrt%283%29%29 = 9%2F25 the area ratio: 9:25 ~ .36
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Interesting to note
18%2F30 = .6 for the perimeters and .36 for the areas; .6^2 = .36
The square of the perimeter ratio = the area ratio