Question

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

• A. $x=-a$
• B. $x=0$
• C. $x=\frac{a}{2}$
• D. $x=3a$

Answer 1

Answer: (A), (D)

The correct options are
A $x=-a$
D $x=3a$

The base of the given triangle is of length $a$.

Now area $=a^2$

$=\frac{base\times height}{2}$

$=\frac{ah}{2}$

Hence, $h=2a$

Now let the third vertex lie on $x=\alpha$, then

$|\alpha -a|=2a$

$\Rightarrow \alpha -a=2a$

$\Rightarrow \alpha =3a$ or

$\Rightarrow \alpha -a=-2a$

$\Rightarrow \alpha =-a$

Hence, the third vertex may lie on either $x=-a$ or $x=3a$.