The triangle above are similar.
What is the perimeter of the blue triangle?
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The triangle above are similar.
What is the perimeter of the blue triangle?
The perimeter of the left triangle: 13+12+5=25+5=30
Therefore, the perimeter of the right triangle divided by 30 is equal to 5.2 divided by 13:
12
If it is known that both triangles are equilateral, are they therefore similar?
Look at the position and angles! In similar triangles, corresponding sides are opposite the same angles. The side labeled 5.2 corresponds to the side labeled 13 because they're in the same relative position.
Similar triangles use multiplication, not addition! The scale factor is a multiplier. If the scale factor is 0.4, then each side of the smaller triangle equals the larger triangle's side × 0.4.
Check if your answer makes sense! If the blue triangle looks smaller but your scale factor is greater than 1, you've flipped it. The scale factor from larger to smaller should be less than 1.
Two ways: Method 1: Find each side length first (12×0.4, 13×0.4, 5×0.4), then add them. Method 2: Find the large triangle's perimeter (30), then multiply by scale factor (30×0.4=12).
Yes! All corresponding sides have the same ratio in similar triangles. Whether you use or any other corresponding pair, you'll get the same scale factor of 0.4.
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