Too many right angles

Construct a rectangle $CNMP$ . We have $CN=MP=21$ , $CP=MN=14$ .

So, $AC=\sqrt{CP^2+AP^2}=\sqrt{14^2+34^2}=26\sqrt{2}$ , implies that $AB=26$ .

Let the length of the side AB be a and the angle MAD be α. Then a=21cosα+13cosα-14sinα and a=21sinα+14cosα+13sinα. From these, we get tanα= $\dfrac{5}{12}$ , sinα= $\dfrac{5}{13}$ and cosα= $\dfrac{12}{13}$ . Therefore a= $\dfrac{338}{13}$ =26