Question

A triangle and a parallelogram have same base and same area. If the sides of the triangle are $20cm,25cm$ and $35cm,$ and the base side is $25$ cm for the triangle as well as the parallelogram, find the vertical height of the parallelogram.

• A. $4\sqrt{6}$ $cm$
• B. $5\sqrt{6}$ $cm$
• C. $4\sqrt{3}$ $cm$
• D. None of the above

Answer 1

The correct option is A $4\sqrt{6}$ $cm$

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$.
For triangle with sides 20 cm, 25 cm and 35 cm, $s=\frac{20+25+35}{2}=40cm$
Area of the triangle $=\sqrt{40(40-20)(40-25)(40-35)}$

$=\sqrt{40\times 20\times 15\times 5}$

$=\sqrt{20\times 2\times 20\times 5\times 3\times 5}$

$=20\times 5\times \sqrt{6}$

$=100\sqrt{6}{cm}^2$

Given, area of the parallelogram $=$ Area of the triangle $=100\sqrt{6}{cm}^2$

Area of a parallelogram $=base\times height$.

So $25\times height=100\sqrt{6}$

$=>height=4\sqrt{6}cm$