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
2 answers:
Answer:
The value of y is 6 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 =
- Simplify the root
∴ NT = 6 units
∵ NT is y
∴ y = 6 units
The value of y is 6 units
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