he perimeters of two similar triangles are 26 cm and 39 cm. The ratio of their areas will be
Question
The perimeters of two similar triangles are 26 cm and 39 cm. The ratio of their areas will be
Solution
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. The ratio of their perimeters is the same as the ratio of their corresponding sides.
Here, the ratio of the perimeters of the two triangles is 26:39.
To simplify this ratio, we divide both numbers by their greatest common divisor, which is 13.
So, the simplified ratio is 2:3.
Therefore, the ratio of their areas will be the square of this ratio, which is (2^2):(3^2) = 4:9.
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