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musiclover10045
The problem says that line TQ is 18 units. The little red line through TQ and TR means that both lines are the same, so TR also equal 18 units.

We can solve for x in the equation for TR :

2x+10 = 18
 Subtract 10 from each side:

2x = 8

Divide both sides by 2:
x = 4

Because TQ and TR are identical, RS and QS are also identical so we can replace X with 4 in the equation for QS:

9(4) -11 = 36 - 11 = 25

RS = 25 units.
akposevictor

Given that right-angle triangles TQS and TRS are congruent, the length of RS is: C. 25 units.

Note:

Right triangles TQS and TRS are congruent triangles, therefore, their corresponding sides are equal.

Thus:

RT = 2x + 10

TQ = 18

RT = TQ

  • Substitute

[tex]2x + 10 = 18[/tex]

  • Find x

[tex]2x = 18 - 10\\\\2x = 8\\\\x = 4[/tex]

  • Also, RS = QS

QS = 9x - 11

  • Plug in the value of x

[tex]QS = 9(4) - 11\\\\QS = 25[/tex]

Therefore,  given that right-angle triangles TQS and TRS are congruent, the length of RS is: C. 25 units.

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https://brainly.com/question/305520

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