Question 254128: solve for the ratio of the areas of 2 similar trianges whose largest sides are 6 cm.and 13 cm.
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! For these similar triangles the ratio of the sides and heights are all 13/6.
Let's say the base and height of the smaller triangle are b1 and h1 respectively. Also let's say the base and height of the larger triangle are b2 and h2 respectively.
Then the area, A1, of the smaller triangle is (b1*h1)/2 and the area of the larger triangle, A2, is (b2*h2)/2.
So the ratio of the two areas is:
A2/A1 = [(b2*h2)/2]/[(b1/h1)/2] = (b2/b1)*(h2/h1).
Since the ratio of the bases and heights are both 13/6 we have:
A2/A1 = (13/6)*(13/6) = 13^2/6^2
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