Answer:
17.7
Explanation:
The perimeter is the sum of the side lengths. Some of these you can figure from your experience with right triangles, or you can use the distance formula to get the same result.
It helps to start by drawing the figure (see attached).
This will show you that segment AB is the hypotenuse of an isosceles right triangle with side lengths 4. Its length will be 4√2 ≈ 5.7.
Segment BC is the hypotenuse of a 3-4-5 right triangle, so is length 5.
Segment CA is a line segment 7 units long.
The sum of these lengths is ...
P = AB +BC +CA = 5.7 +5 +7 = 17.7 . . . . units
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Distance Formula
The distance formula for the distance (d) between points (x1, y1) and (x2, y2) is based on the Pythagorean theorem:
d = √((x2 -x1)² +(y2 -y1)²)
Then the length of AB is ...
d = √((-7-(-11))² +(8-4)²) = √(4² +4²) = √(4²(2)) = 4√2 ≈ 5.6569 ≈ 5.7
And the length of BC is ...
d = √((-4-(-7))² +(4-8)²) = √(3² +(-4)²) = √(9+16) = √25 = 5
You can use the distance formula on CA, but there is no need. The distance is the difference of the x-coordinates: -4-(-11) = 7.