Originally Posted by

**HallsofIvy** Both formulas are correct (although since the problem said "show that the area is $\displaystyle x^2- \frac{7}{2}x+ 3$" the second method would be the "correct answer").

Skeeter pointed out that they both give the same result when x= 5 because, in fact, x **must** be 5!

I'm going to use "A" to represent the common value of AB and BC so that I can use "x" as a variable.

Set up a coordinate system with (0, 0) at B and the positive x axis extending from B through C. Then point A is at (0, A) and point C is at (A, 0). It is easy to see that the line AC is given by y= A- x.

Point E has coordinates (A-3, A- 2). Since it lies on line AC, we must have

A- 2= A- (A- 3)= 3 so A= 3+ 2= 5.

The "x" in the problem **must** be 5 and the two formulas give the same result.