Consider the similar triangle below.
ABC is the per-image and PQR is the image.

Scale factor: 2

PR = 14

Perimeter = 34

Step-by-step explanation:

Similar Triangles

Similar triangles are those who have their corresponding side lengths proportional, i.e. the ratio of the corresponding sides is equal.

The figure shows similar triangles ABC and PQR. We can also see corresponding sides BC and QR have lengths 6 and 12 respectively.

The scale factor is

The rest of the sides can be calculated by using the per-image triangle ABC side lengths and the new-found scale factor. Thus:

PR = AC*2 = 7*2 = 14

PR = 14

PQ = AB*2 = 4*2 = 8

The perimeter of the triangle PRQ is the sum of its side lengths:

P = 12 + 14 + 8 = 34

Answers:

Scale factor: 2

PR = 14

Perimeter = 34

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option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.