Question

Find the perimeter of the image below:

37 units
38 units
39 units
40 units

Answer 1

The correct answer is 39 units.

Parameter is the sum of the lengths of all sides of a polygon. The sides of the polygon are PT, TS, SR, RQ, and QP. To get the length of a side, we use the distance formula:
d =
`\sqrt{ (x_(2) - x_(1)) ^(2) + ( y_2 - y_1)^2}`

Each vertex in the polygon has its corresponding points:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)

So to get the length of side PT, we use the distance formula and the vertices of side PT:
P
`(x_(1) , y_1)` = (-2, 11)
T
`( x_(2) , y_2)` = (8, 7)


`image`

The length of PT is
`√(116)`
The same procedure is done for the other 4 sides and the following are the answers:
TS =
`√(49)`
SR =
`√(50)`
RQ =
`√(61)`
QP =
`√(40)`

And by adding all the sides, you get the perimeter:

`√(116) + √(49) + √(50) + √(61) + √(40) = 38.97`

By rounding off, the answer is 39 units.