The ratio of the areas of two triangles is 4 : 3 and the ratio of their heights is 3 : 4. The ratio of their bases is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 16 : 9
Let the triangles have areas A1 and A2, bases b1 and b2, heights h1 and h2
Area = 1/2 × base × height
A1/A2 = (b1 × h1) / (b2 × h2)
Given A1/A2 = 4/3, h1/h2 = 3/4
(b1/b2) × (h1/h2) = 4/3
(b1/b2) × (3/4) = 4/3
b1/b2 = (4/3) ÷ (3/4) = (4/3) × (4/3) = 16/9