Math Problem Statement
Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9, the length of T Q is 16, and the length of R Q is x. What is the value of x?
12 units 15 units 20 units 24 units
Solution
We have a right triangle with an altitude drawn from to on , forming another right angle. Given:
Step 1: Find
Since and are segments of :
Step 2: Use the Geometric Mean Theorem
The altitude theorem states:
Step 3: Use the Pythagorean Theorem in
Since is a right angle:
Answer:
Would you like a detailed breakdown of any step?
Related Questions:
- What is the altitude theorem in right triangles, and how does it apply here?
- Can you find the length of in this triangle?
- What is the Pythagorean Theorem, and how was it used to find ?
- If was given instead of needing to calculate it, how would that change the approach?
- How can we use similarity of triangles to verify the result?
Tip:
The altitude theorem states that the altitude to the hypotenuse in a right triangle creates two smaller right triangles that are similar to the original triangle.
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Math Problem Analysis
Mathematical Concepts
Right Triangle Geometry
Altitude Theorem
Pythagorean Theorem
Formulas
SQ = ST + TQ
RT^2 = ST * TQ
RQ^2 = RT^2 + TQ^2
Theorems
Geometric Mean Theorem (Altitude Theorem)
Pythagorean Theorem
Suitable Grade Level
Grades 9-11