If AR = 3x + 6, BC = x + 18, and RC = 7, then...

AR = ??
RB = ??

AR = 24 units

RB = 25 units

Step-by-step explanation:

In a rectangle:

In rectangle ABCR

∵ AR and BC are opposite sides

∴ AR = BC

∵ AR = 3x + 6

∵ BC = x + 18

- Equate them to find x

∴ 3x + 6 = x + 18

- Subtract x from both sides

∴ 2x + 6 = 18

- Subtract 6 from both sides

∴ 2x = 12

- Divide both sides by 2

∴ x = 6

Substitute the value of x in the expression of AR to find its length

∵ AR = 3(6) + 6

∴ AR = 18 + 6

∴ AR = 24 units

∵ AC is a diagonal of rectangle ABCR

∴

∵ AR = 24 units

∵ RC = 7 units

∴

∴ AC = 25 units

∵ RB is a diagonal of the rectangle ABCR

∵ The two diagonal of the rectangle are equal in length

∴ AC = RB

∴ RB = 25 units

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

answer   download the app called socratic on your phoner:

step-by-step explanation: