Question

A triangle and a parallelogram have the same base and the same area. If the side of the triangle are 13 cm, 14 cm, and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.

• A. $8cm$
• B. $12cm$
• C. $6cm$
• D. $13cm$

Answer 1

Answer: (C)

$6cm$

Given sides of the triangle are $13cm,14cm,15cm$

We know that the area of the triangle is $\sqrt{s(s-a)(s-b)(s-c)}$

where $a,b,c$ are the sides of the triangle and

$s=\frac{a+b+c}{2}=\frac{13+14+15}{2}=21$

Therefore, the area of the triangle is $\sqrt{21(21-13)(21-14)(21-15)}=\sqrt{7056}=84$ -------(1)

Given that base of the parallelogram is $14cm$

Given that the triangle and the parallelogram have the same area.

Therefore, $\text{area of parallelogram = area of triangle}$

$⟹\text{base * height = area of triangle}$

$⟹\text{14 * height = area of triangle}$

$⟹\text{14 * height = 84}$ (from (1))

$⟹height=\frac{84}{14}=6\text{c}m$