Question

The base of a triangle lies along the line $x=$ and is of length $a$. The area of the triangle is $a^2$, if the vertex lies on the line

• A. $x=0$
• B. $x=-a$
• C. $x=3a$
• D. $x=-3a$

Answer 1

Answer: (B), (C)

$x=-a$
$x=3a$

Let $h$ be the height of the triangle.

Since, the area of the triangle is $a^2$

$\therefore \frac{1}{2}\times a\times h=a^2\Rightarrow h=2a$

Since the base lies along the line $x=a$,

the vertex lies on the line parallel to the base at a distance $2a$ from it.

So, the required lines are

$x=a\pm 2a\Rightarrow x=-a$ or $x=3a$