Question

If the line $3x+4y=p$ makes a triangle of area $24squnits$ with the co-ordinate axes, find the value of $p$.

Answer 1

$3x+4y=p\Rightarrow \frac{x}{p/3}+\frac{y}{p/4}=1$

$\Rightarrow$ Intercepts of line $=\frac{P}{3},\frac{P}{4}$

Area of triangle $=\frac{1}{2}\left(\frac{P}{3}\right)\left(\frac{P}{4}\right)=24$

$\Rightarrow P^2=24\times 24$

$\Rightarrow P=24$