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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
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GPT-5 mini
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15 units
Reason: In a right triangle the altitude to the hypotenuse gives RQ^2 = TQ · SQ. So 20^2 = 16·SQ ⇒ SQ = 400/16 = 25. Then SR^2 + 20^2 = 25^2 ⇒ SR^2 = 625−400 = 225 ⇒ SR = 15.
Reason: In a right triangle the altitude to the hypotenuse gives RQ^2 = TQ · SQ. So 20^2 = 16·SQ ⇒ SQ = 400/16 = 25. Then SR^2 + 20^2 = 25^2 ⇒ SR^2 = 625−400 = 225 ⇒ SR = 15.
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