Question

Find the height of a triangle if base of a triangle is 3 times that of height, given that area of a triangle is 24 $c{m}^2$

• A. 4 cm
• B. 8 cm
• C. 12 cm
• D. 16 cm

Answer 1

The correct option is A 4 cm

Let $x$ be the height of the triangle.
According to given condition
base = 3$\times$height = 3$\times$$x$
Area of triangle = $\frac{1}{2}$$\times$height $\times$base
$\frac{1}{2}$$\times$$x$$\times$3$x$ = 24
$3x^2=48$
$x^2=16$
$x=\pm 4$
Since height cannot be negative
x = 4 cm.
Hence height of the triangle is 4 cm.