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

In The Diagram RSTRST Determine The Length Of RS Show Your Work 100 Points class=

Sagot :

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
mhanifa

Answer:

  • RS = 6 feet

Step-by-step 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
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