Math Problem Statement
What's x
Solution
The image shows two right triangles, and , and the problem states that these triangles are similar: .
Step 1: Use Similarity of Triangles
Since the triangles are similar, the corresponding sides of the triangles are proportional: In the given triangles:
- , , and is the hypotenuse of triangle , which can be calculated using the Pythagorean theorem.
- , , and .
Step 2: Find the Length of
Apply the Pythagorean theorem in :
Step 3: Set up Proportions
Now use the proportion between corresponding sides: Starting with : Simplify to , so:
Step 4: Solve for
Cross-multiply to solve for : Add 6 to both sides: Divide by 2:
Final Answer:
The value of is .
Would you like any further details or have any questions?
Here are 5 related questions to explore:
- How do you verify that two triangles are similar?
- What is the importance of proportionality in similar triangles?
- Can the Pythagorean theorem be applied in non-right triangles?
- What would happen if the triangles weren't similar but still shared some side ratios?
- How does changing one side affect the corresponding sides in similar triangles?
Tip: Always check that your proportionality ratios match between all corresponding sides in similar triangles!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Triangle Similarity
Proportions
Pythagorean Theorem
Algebra
Formulas
Proportions: \( \frac{ST}{AB} = \frac{TU}{BC} = \frac{SU}{AC} \)
Pythagorean theorem: \( a^2 + b^2 = c^2 \)
Theorems
Similarity of Triangles
Pythagorean Theorem
Suitable Grade Level
Grades 9-10