Question 452360
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(6^2-3^2)}}}
h = {{{sqrt(27)}}}
h = {{{3sqrt(3)}}}
Find area 1
A = .5*{{{3sqrt(3)}}}*6
A = {{{3*3sqrt(3)}}}
A = {{{9sqrt(3)}}} sq/cm
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Triangle 2, 10 cm on each side
find the height
h = {{{sqrt(10^2-5^2)}}}
h = {{{sqrt(75)}}}
h = {{{5sqrt(3)}}}
Find  area 2
A = .5*{{{5sqrt(3)}}}*10
A = {{{5*5sqrt(3)}}}
A = {{{25sqrt(3)}}} sq/cm
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Find ratio of the two areas
{{{(9sqrt(3))/(25sqrt(3))}}} = {{{9/25}}} the area ratio: 9:25 ~ .36
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Interesting to note
{{{18/30}}} = .6 for the perimeters and .36 for the areas; .6^2 = .36
The square of the perimeter ratio = the area ratio