Q. 244.0( 23 Votes )

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Answer :

To Find: Height of the parallelogram

Given: Sides of triangle are 26 cm, 28 cm, and 30 cm


Base of parallelogram = 28 cm


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



Area of parallelogram = base × height


Explanation:


Area of triangle = Area of parallelogram


Let us find the area of triangle first.





s = 42 cm




Area = 144√7 cm2


Now,


Area of parallelogram = 28 × height


Therefore,


28 × height = 144√7




Hence, the height of the parallelogram is


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