Question

****WILL GIVE BRAINLIEST TO THE FIRST CORRECT ANSWER****

Answer 1

The answer to this is D. 35.6.

Answer 2

ANSWER
The correct answer is D
$35.6 \: units$



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,

$d = \sqrt{ {(x_2-x_1)}^{2} - {(y_2-y_1)}^{2} }$


Firs let us find the distance between (7, 1) and (-6, 1).

$d_1 = \sqrt{ {(7 - - 6)}^{2} + {(1 - 1)}^{2} }$


This implies that,

$d_1 = \sqrt{ {(7+ 6)}^{2} + {(1 - 1)}^{2} }$




$d_1 = \sqrt{ {(13)}^{2} + {(0)}^{2} }$



$d_1 =13 \: units$



Next, we find the distance between (7,1) and (10,6)


$d_2 = \sqrt{ {(7 - 10)}^{2} + {(1 - 6)}^{2} }$


$d_2 = \sqrt{ {( - 3)}^{2} + {( - 5)}^{2} }$


$d_2 = \sqrt{9 + 25 }$

$d_2 = \sqrt{34} = 5.831 \: units$


Next we find the distance between (-6,1) and (10,6)


$d_3= \sqrt{ {( - 6 - 10)}^{2} + {(1 - 6)}^{2} }$


$d_3= \sqrt{ {( - 16)}^{2} + {( - 5)}^{2} }$



$d_3= \sqrt{256+ 25}$


$d_3= \sqrt{281} = 16.763 \: units$



We now add all the distance to get,

$perimeter = 13 + 16.763 + 5.831$


This implies that,


$perimeter = 35.6 \: units$


to the nearest tenth