Question

Two mutually perpendicular straight lines are drawn from the origin forming an isosceles triangle together with the straight line, $2 x+y=a$. Then the area of the triangle is :

• A. $\frac{a^2}{2}$
• B. $\frac{a^2}{3}$
• C. $\frac{a^2}{5}$
• D. none

Answer 1

Answer: (C)

$p=\left|\frac{0+0-a}{\sqrt{5}}\right|=\frac{a}{\sqrt{5}}$
$\tan 45^{\circ}=\frac{p}{x} \Rightarrow p=x$
Hence area $=\frac{1}{2}(2 x)(p)=p x=p^2=a^2 / 5$