Math Problem Statement
Solution
To solve for , we can set up a proportion based on the similarity of the two triangles. In similar triangles, corresponding side lengths are proportional. The sides labeled in the small triangle are 4 and , and in the larger triangle, they are 10 and 15.
Steps to solve for :
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Set up the proportion:
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Simplify the right side of the proportion:
So the proportion becomes:
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Cross-multiply to solve for :
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Divide by 2:
Answer:
Would you like more details or have any questions?
Here are 5 related questions that expand on this concept:
- How would you solve for if the larger triangle had different side lengths?
- What are other ways to check if two triangles are similar besides using side lengths?
- How can you use proportions to find unknown lengths in non-triangular similar shapes?
- What if both triangles had all unknown side lengths but shared a scale factor? How would you approach this?
- Can proportions be used to solve problems in three-dimensional figures?
Tip: Remember that similar figures have corresponding angles that are equal and corresponding sides that are proportional!
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Math Problem Analysis
Mathematical Concepts
Geometry
Proportions
Similar Figures
Formulas
m / 4 = 15 / 10
Theorems
Properties of Similar Triangles
Suitable Grade Level
Grades 7-8