Question

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 bass 28 cm find the height of the parallelogram

Answer 1

Question:-

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:-

The sides of the triangle are a = 26\ cm,b= 28\ cm\ and\ c =30\ cm.

Then, calculating the area of the triangle:

So, the semi-perimeter of triangle ABE,

s = \frac{a+b+c}{2} = \frac{28+26+30}{2} = 42\ cm.

Therefore, its area will be given by the Heron's formula:

A = \sqrt{s(s-a)(s-b)(s-c)}

= \sqrt{42(42-28)(42-26)(42-30)}

= \sqrt{42(14)(16)(12)} = \sqrt{112896} = 336\ cm^2

Given that the area of the parallelogram is equal to the area of the triangle:

Area\ of\ Parallelogram = Area\ of\ Triangle

\implies base\times corresponding\ height = 336\ cm^2

\implies 28\times corresponding\ height = 336\ cm^2

\implies height = \frac{336}{28} = 12\ cm.

Hence, the height of the parallelogram is 12 cm.

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