Answer:
Option B.) 45 units
Step-by-step explanation:
see the attached figure with letter to better understand the problem
step 1
Determine the coordinates of the corners of the rectangle
Let
A(4,5),B(1,8),C(14,21) and D(17,18)
step 2
we know that
The formula to calculate the perimeter of rectangle is equal to
[tex]P=2(AB+BC)[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the length side AB
[tex]A(4,5),B(1,8)[/tex]
substitute in the formula
[tex]d=\sqrt{(8-5)^{2}+(1-4)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(-3)^{2}}[/tex]
[tex]d_A_B=\sqrt{18}\ units[/tex]
Find the length side BC
[tex]B(1,8),C(14,21)[/tex]
substitute in the formula
[tex]d=\sqrt{(21-8)^{2}+(14-1)^{2}}[/tex]
[tex]d=\sqrt{(13)^{2}+(13)^{2}}[/tex]
[tex]d_B_C=\sqrt{338}\ units[/tex]
Find the perimeter
[tex]P=2(AB+BC)[/tex]
substitute the values
[tex]P=2(\sqrt{18}+\sqrt{338})[/tex]
[tex]P=45\ units[/tex]
