Question

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20. What is the length of Line segment S R? 9 units 12 units 15 units 18 units

Answer 1

The length of the line segment SR is 15 units ⇒ 3rd answer

Step-by-step explanation:

Let us revise the rules in the right angle triangle when we draw the perpendicular from the right angle to the hypotenuse

In triangle ABC

Angle B is a right angle  and AC is the hypotenuse

BD ⊥ AC  ⇒ perpendicular from the right angle to the hypotenuse

• (AB)² = AD × AC
• (BC)² = CD × AC
• (BD)² = AD × CD
• BD × AC = AB × BC

In Δ SRQ

∵ ∠SRQ is a right angle

∴ SQ is the hypotenuse

∵ RT ⊥ SQ

- By using the rules above

∴ (RQ)² = TQ × SQ

∵ RQ = 20 units and TQ = 16 units

- Substitute these values in the rule above

∴ (20)² = 16 × SQ

∴ 400 = 16 × SQ

- Divide both sides by 16

∴ SQ = 25 units

By using Pythagoras theorem in Δ SRQ

∵ (SR)² + (RQ)² = (SQ)²

∵ RQ = 20 units and SQ = 25 units

- Substitute these values in the rule above

∴ (SR)² + (20)² = (25)²

∴ (SR)² + 400 = 625

- Subtract 400 from both sides

∴ (SR)² = 225

- Take √ for both sides

∴ SR = 15 units

The length of the line segment SR is 15 units

Learn more:

You can learn more about right triangles in brainly.com/question/1238144

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Answer 2

Answer: C. 15 units

Step-by-step explanation: I took the test on edge