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.

We need to find the height (altitude) for the triangle by calculating the area for both figures.

Answer: The altitude of the given triangle will be 200 m.

Let us proceed step by step.

Explanation:

From the given data, a triangle and a parallelogram are constructed on the same base, and also their area is equal.

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 = ½ × b × h₁

Area of parallelogram = b × h₂

From the given data, both the areas are equal.

Therefore, ½ × b × h₁  =  b × h₂

We know h₂ = 100

⇒ ½ × b × h₁  =  b × 100

⇒ ½ × h₁  = 100

⇒ h₁ = 100 × 2

⇒ h₁ = 200

Hence, the altitude of the given triangle is 200 m.