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

A 200m

B 300m

C 400m

D 100m

Correct Answer: Option A

Let the triangle and parallelogram have common base b,

let the Altitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then

Area of triangle = \(\frac12\times b\times h1\)

Area of rectangle = b*h2

As per Given,

\(\frac12\ast b\ast h1=b\ast h2\)

\(\frac12\ast b\ast h1=b\ast100\)

h1=200