Question #94e1f

1 Answer
Dec 20, 2014

I don't think the question you're asking is possible, because of the inequality theorem of triangles. I've searched online for a similar problem and found this one. I'm guessing you meant that, so here's a summary of the answer:

The answer is 49/4.
The first thing that's important is that you understand the question. So let's make a drawing:
![web.geogebra.org](useruploads.socratic.org)

We're going to add a line, to do this:
![web.geogebra.org](useruploads.socratic.org)

The length of |EB| = 7, the same as |AD|
The length of |EC| = b-a

Since the angle of E is 90°, we can apply the Pythagorean theorem:

(b-a)^2 + 7^2 = (a+b)^2
If we work this out, we get:
b^2-2ab+a^2+ 49 = a^2 + 2ab +b^2
49 = 4ab
So, what is the product of |AB| and |CD|? it's ab
ab = 49/4

source: maa.org