What is the x-intercept of line l?

[swerve]

In the figure above, the area of the triangle AOB is 30 and the y-intercept of line l is 5. What is the x-intercept of the line l?

A. 25
B. 24
C. 12
D. 6
E. 0

The OA is C.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

[EconomistGMATTutor]

Hello swerve.

Let's take a look at your question.

The area of the triangle is $$A=\frac{AO\cdot OB}{2}.$$ By the other hand, the y-intercept of line l is 5, it implies that $$OA=5\ and\ OB=x.$$ Replacing this on the area we will get: $$A=\frac{5\cdot x}{2}=30\ \leftrightarrow\ 5x=60\ \leftrightarrow\ x=12.$$ So, the correct answer is C.

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.