A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is:

Question: A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is:

Solution:
In this question, we will denote ‘b’ as the base h1 and h2 as the altitudes of the triangle and parallelogram respectively.

Then, according to the data in the question:

½ × b × h1 = b × h2
⇒ h1 = 2 h2
⇒ h1 = 2 × 100 = 200m

∴ The altitude of the triangle is 200m.