Question

If base and the altitude of a triangle are $(3m+2n)$ cm and $(3m-4n)$ cm respectively, then the area of the triangle when $m=2$ and $n=1$ is _____.

• A. $8c{m}^2$
• B. $16c{m}^2$
• C. $4c{m}^2$
• D. $12c{m}^2$

Answer 1

The correct option is A $8c{m}^2$

Given:
Base of the triangle
= $(3m+2n)$ cm

Altitude of the triangle
= $(3m-4n)$ cm

By substituting the value of m and n, we get:
Base of the triangle
$=(3m+2n)$
$=3\times 2+2\times 1$
$=6+2=8cm$
Altitude of the triangle
$=(3m-4n)$
$=3\times 2-4\times 1$
$=6-4$
$=2cm$

$\text{Required area}$
$=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 8\times 2$
$=8c{m}^2$