Question

A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is $100m$ in length, then find the altitude of the triangle ?

Answer 1

Hint: Here in this question, we are given a triangle and a parallelogram sharing the same base. Both the polygons have equal areas. The altitude of the parallelogram is given to us in the question itself. We have to find the altitude of the triangle sharing the base with parallelogram. The question revolves around the concepts of mensuration. One must know the formulae for the area of triangle and parallelogram in order to solve the given problem.

Complete step-by-step answer:
In the given problem, we are provided with a triangle and a parallelogram.
A triangle is a polygon with three edges and three vertices.
The formula for finding the area of a triangle is $\left( {\dfrac{{Base \times Altitude}}{2}} \right)$.
A parallelogram is a two dimensional shape with two pairs of parallel sides.
 The formula for finding the area of a parallelogram is $\left( {Base \times Altitude} \right)$.
So, we are given that both the triangle and the parallelogram share the same base. Hence, both the shapes have equal bases. The altitude of the parallelogram is $100m$ in length.
Hence, Area of parallelogram is $\left( {Base \times 100m} \right)$.
Area of the triangle is $\left( {\dfrac{{Base \times Altitude}}{2}} \right)$.
Also, we are given that the area of the two polygons are equal. So, we can equate the formulae for finding the areas of the two polygons.
So, equating both, we get,
$ \Rightarrow \left( {\dfrac{{Base \times Altitude}}{2}} \right) = \left( {Base \times 100m} \right)$
We know that the value of base for both polygons is equal. Hence, cancelling the term from both sides of the equation, we get,
$ \Rightarrow \left( {\dfrac{{Altitude}}{2}} \right) = 100m$
Simplifying the equation, we get,
$ \Rightarrow Altitude = 2 \times 100m$
$ \Rightarrow Altitude = 200m$
Hence, the length of the altitude of the triangle is $200\;m$.
So, the correct answer is “$200\;m$”.

Note: Generally the area is the region occupied by the thing. The area of a polygon is defined as the region occupied by the shape. One must take care while handling the calculations so as to be sure of the answer.