Answer:
[tex]2\sqrt{29}+\sqrt{53}+5[/tex]
Step-by-step explanation:
The distance between A and B is a vertical distance of [tex]2[/tex] and a horizontal distance of [tex]5[/tex]. By the Pythagorean Theorem, [tex]AB=\sqrt{2^2+5^2}=\sqrt{29}[/tex].
The distance between B and C is [tex]5[/tex] by counting squares.
The distance between C and D is a vertical distance of [tex]2[/tex] and a horizontal distance of [tex]7[/tex]. By the Pythagorean Theorem, [tex]CD=\sqrt{2^2+7^2}=\sqrt{53}[/tex].
The distance between D and A is a vertical distance of 5 and a horizontal distance of [tex]2[/tex]. By the Pythagorean Theorem, [tex]DA=\sqrt{5^2+2^2}=\sqrt{29}[/tex].
So, the answer is [tex]\boxed{2\sqrt{29}+\sqrt{53}+5}[/tex]
