Question

A triangle and a parallelogram have the 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. 14 cm
• B. 16 cm
• C. 10 cm
• D. 12 cm

Answer 1

The correct option is D

12 cm

The triangle and the parallelogram lie on the same base of 28 cm. The other sides of the triangle are 26 cm and 30 cm.

Semi-perimeter of the triangle:
$s=\frac{(a+b+c)}{2}=\frac{(26+28+30)}{2}=\frac{84}{2}=42\text{cm}.$

Area of Triangle
$ar\left(△\right)=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{42(42-26)(42-28)(42-30)}=\sqrt{42\times 16\times 14\times 12}=\sqrt{14\times 3\times 16\times 14\times 3\times 4}ar\left(△\right)=14\times 3\times 4\times 2=336{\text{cm}}^2$

Since, $ar\left(△\right)=ar\left(\text{parallelogram}\right)=336{\text{cm}}^2$

Let, Base of Paralellogram = $b_p=28\text{cm}$
Height of Paralellogram = $h_p$
$\therefore ar\left(\text{parallelogram}\right)=b_p\times h_p$

$b_p\times h_p=336\Rightarrow h_p=\frac{336}{28}{\text{cm}}^2=12\text{cm}$

Height of Paralellogram is 12 cm.