Question

Find the height of an acute triangle if area of the triangle is $49{\text{unit}}^2$ and the base of this triangle is twice the height of the triangle.

• A. 28 unit
• B. 21 unit
• C. 14 unit
• D. 7 unit

Answer 1

The correct option is D 7 unit

Given,
Area of the triangle $=49{\text{unit}}^2$
$\Rightarrow$ Let, the height of a triangle be $AD=h$

Given: The base of a $△$ ABC is twice the height of the traingle.
$\Rightarrow$ The base of a triangle is $BC=2h.$
Let's consider a triangle $\Delta ABC$ as shown.
Here $BC=2h$ and $AD=h$
As we know,
Area of$△ABC=\frac{1}{2}\times \text{BC}\times \text{AD}$

$49=\frac{1}{2}\times 2h\times h$

$49=h\times h$

$h^2=49$

$h=\sqrt{4}=\sqrt{7\times 7}=7unit$

Hence, the height of a triangle is 7 unit.
Option (d) is correct.