Question

A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitudes of the parallelogram is $150m$ find the altitude of the triangle.

Answer 1

Let the triangle and parallelogram have common base $b$,

let the Altitude of triangle is $h_1$ and of parallelogram is $h_2$(which is equal to $150$m), then

Area of triangle $=\frac{1}{2}\times b\times h_1$

Area of rectangle $=b\times h_2$

As per question $\frac{1}{2}\times b\times h_1=b\times h_2$

$\Rightarrow \frac{1}{2}\times b\times h_1=b\times 150\times h_1=150\times 2=300$m