Question

The height of a right triangle is thrice its base. The area is 384 sq.cm. What is the measurement of the base?

Answer 1

Step-by-step explanation:

refer to the attachment

Answer 2

The measurement of the base of the triangle is 16cm

Given :

The height of the triangle = thrice its base

The area of the triangle = 384sq.cm

To Find :

Measurement of the base

Formula Applied :

$area = \frac{a \times b}{2}$

Solution :

Let the height of the triangle be a.

Let the base of the triangle be b.

It's given that height is thrice the base. Hence

height = 3 × base

$a = 3b \: ........(1)$

We know that $area = \frac{a \times b}{2}$

hence , $384 = \frac{a \times b}{2}$

Substitute (1) in the formula

$384 \times 2 = 3b \times b$

$3 {b}^{2} = 768$

${b}^{2} = \frac{768}{3}$

${b}^{2} = 256$

$b = 16$