If you create an imaginary rectangle of vertices ABCX (with X the imaginary vertex), you get a triangle AXD. Then, you can use Pythagoras:

\((AX)^2 + (XD)^2 = (AD)^2\)

\(24^2 + (XD)^2 = 26^2\)

doing some math:

XD = 10.

but they are asking for CD, therefore,

(remember that XC = AB = 4)
CD = XD - XC,
CD = 10 - 4
CD = 6,

In conclusion, A<B, option B.

A quick solution is to realize that \(BC\) and \(AD\) are parts of a 5:12:13 right triangle.

To see it more clearly, drop a line down from point A and extend point C out to meet it. Essentially, what you have is \(BC\) being the height of this new triangle and \(AD\) being the new hypotenuse.

Since we have a 5:12:13 triangle, we know that new length of \(CD\) plus the added length must be 10 (10:24:26). That added length is actually the length of \(AB\), which is 4.

10 - 4 = 6, which is the length of \(CD\), giving the answer B.

Best solution.

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