ANSWER
The correct answer is D
[tex]35.6 \: units[/tex]
EXPLANATION
We need to use the distance formula to determine the length of all sides and then add them up.
The distance formula is given by,
[tex]d = \sqrt{ {(x_2-x_1)}^{2} - {(y_2-y_1)}^{2} } [/tex]
Firs let us find the distance between (7, 1) and (-6, 1).
[tex]d_1 = \sqrt{ {(7 - - 6)}^{2} + {(1 - 1)}^{2} } [/tex]
This implies that,
[tex]d_1 = \sqrt{ {(7+ 6)}^{2} + {(1 - 1)}^{2} } [/tex]
[tex]d_1 = \sqrt{ {(13)}^{2} + {(0)}^{2} } [/tex]
[tex]d_1 =13 \: units[/tex]
Next, we find the distance between (7,1) and (10,6)
[tex]d_2 = \sqrt{ {(7 - 10)}^{2} + {(1 - 6)}^{2} } [/tex]
[tex]d_2 = \sqrt{ {( - 3)}^{2} + {( - 5)}^{2} } [/tex]
[tex]d_2 = \sqrt{9 + 25 } [/tex]
[tex]d_2 = \sqrt{34} = 5.831 \: units[/tex]
Next we find the distance between (-6,1) and (10,6)
[tex]d_3= \sqrt{ {( - 6 - 10)}^{2} + {(1 - 6)}^{2} } [/tex]
[tex]d_3= \sqrt{ {( - 16)}^{2} + {( - 5)}^{2} } [/tex]
[tex]d_3= \sqrt{256+ 25} [/tex]
[tex]d_3= \sqrt{281} = 16.763 \: units[/tex]
We now add all the distance to get,
[tex]perimeter = 13 + 16.763 + 5.831[/tex]
This implies that,
[tex]perimeter = 35.6 \: units[/tex]
to the nearest tenth
