If two triangles are similar, and the lengths of the sides of the first triangle

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Question: If two triangles are similar, and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the corresponding sides of the second triangle if the shortest side is 6?

Options:

6, 8, 10
9, 12, 15
12, 16, 20
15, 20, 25

Correct Answer: 6, 8, 10

Solution:

The ratio of the sides of similar triangles is constant. If the shortest side of the first triangle (3) corresponds to 6, then the sides are scaled by a factor of 2. Thus, the other sides are 4*2=8 and 5*2=10.

If two triangles are similar, and the lengths of the sides of the first triangle

Practice Questions

If two triangles are similar, and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the corresponding sides of the second triangle if the shortest side is 6?

6, 8, 10
9, 12, 15
12, 16, 20
15, 20, 25

Questions & Step-by-Step Solutions

If two triangles are similar, and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the corresponding sides of the second triangle if the shortest side is 6?

Step 1: Identify the sides of the first triangle. The sides are 3, 4, and 5.
Step 2: Identify the shortest side of the first triangle, which is 3.
Step 3: Identify the shortest side of the second triangle, which is given as 6.
Step 4: Determine the scale factor by dividing the shortest side of the second triangle (6) by the shortest side of the first triangle (3). This gives us 6 / 3 = 2.
Step 5: Use the scale factor to find the lengths of the other sides of the second triangle. Multiply the other sides of the first triangle by the scale factor (2).
Step 6: Calculate the second side: 4 * 2 = 8.
Step 7: Calculate the third side: 5 * 2 = 10.
Step 8: The lengths of the corresponding sides of the second triangle are 6, 8, and 10.

Similarity of Triangles – Understanding that similar triangles have proportional sides.
Scaling Factor – Calculating the scaling factor based on the lengths of corresponding sides.

If two triangles are similar, and the lengths of the sides of the first triangle

What’s inside this PDF?

If two triangles are similar, and the lengths of the sides of the first triangle

Practice Questions

Questions & Step-by-Step Solutions

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