Two Triangles Are Similar.Aside Of One Is 2 units long .the corresponding sides of the other is 5 units long. what is the ratio of a. their perimeters? b. their areas?
P1/P2 = 2/5, A1/A2 = (2/5)^2 = 4/25.
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To find the ratio of the perimeters of two similar triangles, we can simply compare the lengths of their corresponding sides.
Given that one side of the first triangle is 2 units long and the corresponding side of the second triangle is 5 units long, we can determine the ratio of their perimeters.
Let's denote the ratio of the perimeters as r.
a. Ratio of Perimeters:
The ratio of perimeters is equal to the ratio of their corresponding sides. So, we have:
r = (Corresponding side of the second triangle) / (Corresponding side of the first triangle)
Since the corresponding sides are given as 5 units and 2 units respectively:
Therefore, r = 5 / 2 = 2.5
So, the ratio of their perimeters is 2.5.
b. Ratio of Areas:
The ratio of areas between two similar triangles is equal to the square of the ratio of their corresponding sides.
Let's denote the ratio of the areas as r².
r² = [(Corresponding side of the second triangle) / (Corresponding side of the first triangle)]²
Again, substituting the given values, we get:
r² = (5 / 2)² = 25 / 4 = 6.25
So, the ratio of their areas is 6.25.
In summary:
a. The ratio of their perimeters is 2.5.
b. The ratio of their areas is 6.25.