Question

A triangle and a parallelogram have the same base and same base and 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.

• A. $8$ cm
• B. $10$ cm
• C. $12$ cm
• D. $14$ cm

Answer 1

The correct option is C $12$ cm

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$s=\frac{a+b+c}{2}$

$\Rightarrow s=\frac{26+28+30}{2}\Rightarrow s=42$

Area of triangle$=\sqrt{42\times 16\times 14\times 12}$

$=336$

Area of parallelogram = Area of triangle

$\Rightarrow h\times b=336$

$h=\frac{336}{28}$

$\Rightarrow h=12$cm