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

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

∵ 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

correct

step-by-step explanation: