If the perimeters of two similar triangles are in the ratio of 4 : 7, and the sum of the areas is 195 cm2, then what is of the difference between the areas (in cm2) of the two triangles?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 33.
Let the areas of the two triangles be 16x and 49x (since the ratio of areas of similar triangles is the square of the ratio of their perimeters).
Given, 16x + 49x = 195 ⇒ 65x = 195 ⇒ x = 3
Therefore, the areas of the two triangles are 48 cm² and 147 cm².
The difference between the areas = 147 - 48 = 99 cm².
1/3 of the difference = 99/3 = 33 cm².