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A triangle and a parallelogram have equal areas and equal bases. If the altitude of the triangle is k times the altitude of the parallelogram, then what is the value of k?

A triangle and a parallelogram have equal areas and equal bases. If the altitude of the triangle is k times the altitude of the parallelogram, then what is the value of k? Correct Answer 2

Given:

A triangle and a parallelogram have equal areas and equal bases.

The altitude of the triangle is k times the altitude of the parallelogram.

Formula used:

Area of parallelogram = base × height

Area of triangle = (1/2) × base × height

Calculation:

Let the length of the base of a triangle and a parallelogram be “b”.

According to the question,

Base of triangle = Base of parallelogram = b.

If “a” is the altitude of the parallelogram,

Then, altitude of the triangle = Ka.

Again, It is given that area of a parallelogram is equal to the area of the triangle,

⇒ ab = 1/2 × ka × b

⇒ k = 2

∴ The value of k is 2.

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