A triangle and parallelogram are constructed on the same base such that their area is equal. If the altitude of the parallelogram is 100m, then find the altitude of the triangle.
Answer: The altitude of the given triangle will be 200 m.
Let us proceed step by step.
We have to find the height of the triangle.
Let us assume the base of the triangle and parallelogram as b as they are constructed on the same base
Let the altitude of the triangle is h1 and of the parallelogram is h2, then
Area of triangle = 1 / 2 × b × h1
Area of parallelogram = b × h2
From the given data, both the areas are equal.
Therefore, 1 / 2 × b × h1 = b × h2
We know h2 = 100
⇒ 1 / 2 × b × h1 = b × 100
⇒ 1 / 2 × h1 = 100
⇒ h1 = 100 × 2
⇒ h1 = 200