Math Problem Statement
Solution
In the given problem, Triangle 2 is a scale drawing of Triangle 1, meaning the two triangles are similar. Similar triangles have proportional sides. Let's use this information to find the length of side in Triangle 2.
Information from the image:
-
Triangle 1:
- Short leg = 12 cm
- Long leg = 16 cm
- Hypotenuse = 20 cm
-
Triangle 2:
- Short leg = 30 cm
- Long leg =
- Hypotenuse = 50 cm
Since the triangles are similar, the ratio of corresponding sides is constant. The ratio between the hypotenuses is:
So, the sides of Triangle 2 are scaled by a factor of compared to Triangle 1. We can apply this scale factor to the long leg (16 cm) of Triangle 1 to find :
Thus, the length of side is 40 cm.
Would you like further details or have any other questions? Here are some related questions you could explore:
- How can we verify that the triangles are indeed similar?
- How would you find the area of both triangles?
- What is the ratio of the areas of Triangle 1 and Triangle 2?
- If the short leg of Triangle 1 was increased, how would that affect the dimensions of Triangle 2?
- How does the Pythagorean theorem apply to both triangles?
Tip: When working with similar triangles, remember that all corresponding angles are equal, and corresponding sides are proportional.
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Math Problem Analysis
Mathematical Concepts
Geometry
Proportions
Similar Triangles
Formulas
Proportion of similar triangles: (corresponding side 1)/(corresponding side 2) = (scale factor)
Theorems
Pythagorean Theorem
Similarity Theorem
Suitable Grade Level
Grades 7-8
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