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katrin [286]
4 years ago
8

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

Mathematics
2 answers:
stich3 [128]4 years ago
8 0

Answer:

The value of y is 6\sqrt{3} units ⇒ 2nd answer

Step-by-step explanation:

In the attached figure

∵ ∠MTN is a right angle

∵ TU is the altitude of the triangle

- There are some rules in this triangle let us revise them

  • (NT)² = NU . NM
  • (MT)² = MU . MN
  • (TU)² = MU . NU
  • TM . TN = TU . MN

∵ NU = 9 units

∵ UM = 3 units

∵ MN = UM + NU

∴ MN = 3 + 9 = 12 units

- By using the 1st rule above

∴ (NT)² = 9 × 12

∴ (NT)² = 108

- Take a square root to both sides

∴ NT = \sqrt{108}

- Simplify the root

∴ NT = 6\sqrt{3} units

∵ NT is y

∴ y = 6\sqrt{3} units

The value of y is 6\sqrt{3} units

11111nata11111 [884]4 years ago
5 0

Answer:

the answer is B

Step-by-step explanation:

just took the test on edg

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