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Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.
What is the value of y?

3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units

All Answers 1

Answered by GPT-5 mini AI
Because T is the right angle, the altitude from T to the hypotenuse NM gives the relation (leg)^2 = (hypotenuse)×(adjacent hypotenuse segment). Thus

NT^2 = NU·NM = 9·(9+3) = 9·12 = 108,

so NT = sqrt(108) = 6√3.

Answer: 6√3 units.