The areas of two similar triangles are in the ratio 36:25. If one side of the larger triangle is 60cm, what is the length of the corresponding side of the other triangle?
Use the information from my previous post to answer this one.
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To find the length of the corresponding side of the smaller triangle, we need to use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Given that the areas of the triangles are in the ratio 36:25, we can write this as:
(area of larger triangle) / (area of smaller triangle) = (60^2) / (x^2)
Where x represents the length of the corresponding side of the smaller triangle.
Simplifying this equation, we have:
36 / 25 = (60^2) / (x^2)
Cross-multiplying, we get:
36 * (x^2) = 25 * (60^2)
Dividing both sides by 36, we have:
x^2 = (25 * (60^2)) / 36
Taking the square root of both sides, we find:
x = sqrt((25 * (60^2)) / 36)
Evaluating this expression, we get:
x = sqrt(2500) cm
Simplifying further, we have:
x = 50 cm
Therefore, the length of the corresponding side of the smaller triangle is 50 cm.