SOLUTION: Two triangles are similar. Two corresponding sides measure 10cm and 15cm, respectively. The area of the smaller triangle is 30cm^2. What is the area of the larger triangle?

Question 878439: Two triangles are similar. Two corresponding sides measure 10cm and 15cm, respectively. The area of the smaller triangle is 30cm^2. What is the area of the larger triangle?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the triangles are similar, then all the corresponding sides are proportional by the same ratio as one of the sides.
this means that the ratio of sides of the bigger triangle to the smaler triangle is equal to 15/10 = 1.5.
this applies to all corresponding parts, including the height.
the area of the triangle is equal to 1/2 * base * height.
that would be the area of the smaller triangle.
the area of the bigger triangle would be equal to 1/2 * 1.5 * base * 1.5 * height which would make the area of the bigger triangle equal to 1.125 * base * height.
the ration of the area of the bigger triangle to the smaller triangle would therefore be equal to 1.125 * base * height / .5 * base * height which makes the ratio of the areas equal to 1.125 / .5 = 2.25.
1.5 * 1.5 is equal to 2.25
this means that the ratio of the area is equal to the ratio of the sides squared.
this just happens to be the formula that is generally applicable.
in a 2 dimensional figures, the ratio of the area of similar figures is equal to the ratio of the sides squared.
in a 3 dimensional figure, the ratio of the volume of similar figures is equal to the ratio of the sides cubed.
here's a reference:
http://www.regentsprep.org/Regents/math/geometry/GP11/LMoresimilar.htm
in your figure the ratio of the sides was 15:10 which i simplified to 1.5 of 1.5:1
the ratio of the areas is therefore 15^2/100^2 which is equal to 225/100 which i simplified to 2.25.

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