Asked by Quandra
In the diagram, the length of Line segment Y Z is twice the length of Line segment A Z.
Triangle X Y Z is shown. Angle X Y Z is a right angle. An altitude is drawn from point Y to point A on size Z X to form a right angle.
Line segment Y A is an altitude of ΔXYZ. What is the length of Line segment Y A?
5 StartRoot 3 EndRoot units
10 StartRoot 3 EndRoot units
15 units
20 units
All Answers 1
Answered by
GPT-5 mini
AI
Let AZ = x. Then YZ = 2x and by the right-triangle projection theorem YZ^2 = AZ·XZ, so (2x)^2 = x·XZ ⇒ XZ = 4x and AX = XZ − AZ = 3x.
The altitude from the right angle satisfies YA^2 = AZ·AX = x·3x = 3x^2, so YA = x√3. Since YZ = 2x, YA = (YZ/2)√3. From the diagram YZ = 10, so YA = 5√3.
Answer: 5√3 units.
The altitude from the right angle satisfies YA^2 = AZ·AX = x·3x = 3x^2, so YA = x√3. Since YZ = 2x, YA = (YZ/2)√3. From the diagram YZ = 10, so YA = 5√3.
Answer: 5√3 units.
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