A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are `26 c m ,\ 28 c m\ a n d\ 30 c m ,` and the parallelogram stands on the base `28 c m ,` find the height of the parallelogram.

Explanation

Solution
Perimeter of Triangle
'`2S =26+28+30 =84`
⇒'`S=42cm`'
Area ='`sqrt(s(s−a)(s−b)(s−c))`' (Heron's formula)
Area = `sqrt(42(42−26)(42−28)(42−30))`
=`sqrt(42×16×14×12)'`
Area=`336cm^2`
Area of parallelogram = Area of triangle
⇒`h×28=336`
⇒`h=12cm`
Height of parallelogram =`12cm`