Find the ratio of the areas of two triangles if the sides of one are 36cm, 24cm

| May 4, 2021 | education

Find the ratio of the areas of two triangles if the sides of one are 36cm, 24cm, 42cm, the sides of the other are 4: 6: 7, and its smaller side is 8cm.

Let the lengths of the sides of the second triangle be 4 * X cm, 6 * X cm, 7 * X cm.Since its smaller side is 8 cm, then 4 * X = 8, X = 8/4 = 2.

6 * X = 6 * 2 = 12 cm.

7 * X = 7 * 2 = 14 cm.

Let’s find the ratio of the sides of the triangles.

8/24 = 1/3.

12/36 = 1/3.

14/42 = 1/3.

Since the ratio of the lengths of the sides of the triangles are equal, these triangles are similar in three proportional sides, and the coefficient of their similarity is K = 1/3.

The ratio of the areas of similar triangles is equal to the coefficient of their similarity.

Then S1 / S2 = K2 = 1/9.

Answer: The area ratio is 1/9.



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