Question 919664: Two triangles are similar. The area of the smaller one is 2133mm and the area of the larger one is 4800mm. One side of the smaller triangle is 60mm and the corresponding side in the large one is 90mm. Calculate the side opposite in both triangles.
I found the ratio of their sides but i really dont know what to do next. I would really appreciate your help. Thank you.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Since we are not given an angle for each triangle, we assume we are working with right triangles.
We use the formula for the area of a triangle, A = 1/2*b*h. Let the base be equal to 60 or 90 and we have for the two triangles,
2133 = 1/2 * 60 * h1
60h1 = 4266
h1 = 71.1
4800 = 1/2 * 90 * h2
90h2 = 9600
h2 = 106.7
note that 60/90 = 2/3 and 71.1 / 106.7 = 2/3
we want the side opposite 90 degrees which is the hypotenuse
note formula to use is a^2 + b^2 = c^2
60^2 + 71.1^2 = c1^2
c1^2 = 8655.21
c1 = 93.03
90^2 + 106.7^2 = c2^2
c^2 = 19484.89
c2 = 139.59
note that 93.03 / 139.59 = 2/3
the sides opposite the 90 degree angle for each triangle are 93.03 and 139.59
and the sides for each triangle are
60, 71.1, 93.03 and 90, 106.7, 139.59
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