Similar Triangles Perimeter Problem: Calculate Using 3.5, 1.5, and 4 Units

Similar Triangles with Scale Factor Calculations

3.51.54146

The triangles above are similar.

Calculate the perimeter of the larger triangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perimeter of the second triangle
00:03 The triangle's perimeter equals the sum of its sides
00:10 This is triangle 1's perimeter
00:15 Similar triangles according to given data
00:21 The ratio of triangles' perimeters equals the similarity ratio
00:26 Let's substitute appropriate values and solve for the perimeter
00:32 Let's isolate P2
00:46 Let's substitute perimeter 1's value
00:53 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

3.51.54146

The triangles above are similar.

Calculate the perimeter of the larger triangle.

2

Step-by-step solution

We calculate the perimeter of the smaller triangle (top):

3.5+1.5+4=9 3.5+1.5+4=9

Due to their similarity, the ratio between the sides of the triangles is equal to the ratio between the perimeters of the triangles.

We will identify the perimeter of the large triangle using x x :

x9=143.5 \frac{x}{9}=\frac{14}{3.5}

3.5x=14×9 3.5x=14\times9

3.5x=126 3.5x=126

x=36 x=36

3

Final Answer

36

Key Points to Remember

Essential concepts to master this topic
  • Similarity Rule: Corresponding sides have the same ratio in similar triangles
  • Scale Factor: Calculate 143.5=4 \frac{14}{3.5} = 4 to find enlargement ratio
  • Perimeter Check: Multiply smaller perimeter by scale factor: 9 × 4 = 36 ✓

Common Mistakes

Avoid these frequent errors
  • Adding side lengths instead of using ratios
    Don't just add the larger sides (14 + 6) = wrong perimeter! This ignores the third side and similarity properties. Always find the scale factor first, then multiply the entire smaller perimeter by this ratio.

Practice Quiz

Test your knowledge with interactive questions

If it is known that both triangles are equilateral, are they therefore similar?

FAQ

Everything you need to know about this question

How do I know which sides correspond to each other?

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Look for matching colors or similar positions in the diagram. The side labeled 3.5 corresponds to the side labeled 14 because they're both the longest sides of their respective triangles.

What if I get different ratios from different pairs of sides?

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If the triangles are truly similar, all ratios must be equal. Getting different ratios means either the triangles aren't similar or you made a calculation error - double-check your work!

Can I use any pair of corresponding sides to find the scale factor?

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Yes! Any pair of corresponding sides will give you the same scale factor. Choose the pair that's easiest to calculate with - often the ones with simpler numbers.

Why multiply the whole perimeter instead of calculating each side separately?

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Since all sides are enlarged by the same scale factor, the perimeter is also enlarged by that same factor. This saves time: 9 × 4 = 36 is much faster than finding each side individually!

What if the scale factor is a fraction?

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That just means the 'larger' triangle is actually smaller! The process is identical - multiply the original perimeter by your fractional scale factor to get the new perimeter.

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