Question

In the diagram, △RST∼△R′S′T′. Determine the length of RS. Show your work.
100 points!

Answer 1

Answer: 6 feet


Explanation: Since the triangles are similar, we can use the proportion 9/4=(12x+2)/(5x+1).

Cross multiplying 9*(5x+1) and 4*(12x+2) gives us 45x+9=48x+8.

Solving for x gives us 1/3.

You can check your work by plugging in x for the two equations, which gives us 6 (RS) and 8/3 (R’S’)

The scale factor is 4/9 (k) from 9k=4

6*4/9=8/3 and (8/3)/(4/9)=6

Answer 2

• RS = 6 feet

Explanation:

Use ratios of corresponding sides:

• TS/T'S' = RS/R'S'

Substitute and solve for x:

• 9/4 = (12x + 2)/(5x + 1)
• 9(5x + 1) = 4(12x + 2)
• 45x + 9 = 48x + 8
• 48x - 45x = 9 - 8
• 3x = 1
• x = 1/3

Find the length of RS:

• RS = 12x + 2 = 12(1/3) + 2 = 4 + 2 = 6 feet