According to the property of a rectangle, opposite sides are parallel and equal.
Thus,
[tex]\begin{gathered} AD\cong BC \\ DC\cong AB \end{gathered}[/tex]
From the above congruencies, we can conclued that
[tex]\begin{gathered} AB=34 \\ BC=23 \end{gathered}[/tex]
Also, the property of a rectangle states that all angles in the rectangle are right angle, this can be illustrated in the diagram below
Using the Pythagorean theorem, BD can be expressed as
[tex]\begin{gathered} BD^2=BC^2+DC^2 \\ BD=\sqrt[]{BC^2+DC^2} \end{gathered}[/tex][tex]\begin{gathered} BC=23 \\ DC=34 \end{gathered}[/tex][tex]\begin{gathered} BD=\sqrt[]{23^2+34^2} \\ BD=41.0 \end{gathered}[/tex]
Hence, AB = 34, BC=23 and BD= 41.0
