Math Problem Statement
Solution
To find the value of the missing side in the similar triangles, we can use the property that the ratios of corresponding sides of similar triangles are equal.
Given triangles:
- Larger triangle sides: 12, 20
- Smaller triangle sides: 3,
The ratio of the corresponding sides should be equal. Therefore, we can set up the following proportion:
Now, solve for :
- Simplify the ratio on the left side:
- Set up the equation:
- Cross-multiply to solve for :
- Divide both sides by 4:
So, the value of the missing side is .
Would you like any more details or have any questions?
Here are 5 related questions that expand on this information:
- What are the properties of similar triangles?
- How can you verify that two triangles are similar?
- How do you find the scale factor between two similar triangles?
- Can the method used here apply to other geometric shapes? If so, how?
- How does changing the lengths of sides in one triangle affect the other in similar figures?
Tip: When working with proportions, always ensure the ratios are set up with corresponding sides from each figure or shape.
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Math Problem Analysis
Mathematical Concepts
Similar Triangles
Proportions
Formulas
Ratio of corresponding sides: (larger side in larger triangle / corresponding side in smaller triangle) = (other larger side in larger triangle / corresponding smaller side)
Theorems
Corresponding sides of similar triangles are proportional
Suitable Grade Level
Grades 6-8
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