Question 94e1f

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 $\frac{49}{4}$.
The first thing that's important is that you understand the question. So let's make a drawing:

We're going to add a line, to do this:

The length of $| E B | = 7$, the same as $| A D |$
The length of $| E C | = b - a$

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

${\left(b - a\right)}^{2} + {7}^{2} = {\left(a + b\right)}^{2}$
If we work this out, we get:
${b}^{2} - 2 a b + {a}^{2} + 49 = {a}^{2} + 2 a b + {b}^{2}$
$49 = 4 a b$
So, what is the product of $| A B |$ and $| C D |$? it's $a b$
$a b = \frac{49}{4}$

source: maa.org