Video Explanation

Text Explanation

First, we need to think about this geometric situation.  Point A is at the origin.  Point B is somewhere on the y-axis, so AB is a vertical line in the xy-plane.  If angle ABC = 90°, the only way a line can be perpendicular to a vertical line is by being horizontal.  Segment BC must be horizontal. 

If BC is horizontal, this means that point B and point C must have the same y-coordinate, because any two points on the same horizontal line in the coordinate plane have the same y-coordinate.   This fact allows us to set up an equation. 

4a – 5 = 2a + 6

2a = 11

We can leave this in terms of 2a, because all the expression have either 2a or 4a in them.  Thus, we know

A = (0, 0)

B = (0, 2(2a) – 5) = (0, 22 – 5) = (0, 17)

C = (2a + 1, 2a + 6) = (11 + 1, 11 + 6) = (12, 17)

Here's a scaled diagram.

Even a rough sketch would be enough: we know that leg AB = 17 and leg BC = 12, and these can be consider the base and the height.  (It actually doesn't matter which we call the base and which we call the height.)    

Area 

Answer = (A)