If two triangles are similar, and the lengths of the sides of the first triangle
Practice Questions
Q1
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 ratio is 2:3?
4, 5, 6
6, 8, 10
2, 3, 4
1.5, 2, 2.5
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 ratio is 2:3?
Step 1: Understand that similar triangles have sides in a specific ratio. Here, the ratio is 2:3.
Step 2: Identify the lengths of the sides of the first triangle, which are 3, 4, and 5.
Step 3: To find the lengths of the corresponding sides of the second triangle, we need to use the ratio 2:3.
Step 4: Set up the proportion for each side. For the first side (3), we can write: (3 / x) = (2 / 3).
Step 5: Solve for x (the corresponding side in the second triangle) by cross-multiplying: 3 * 3 = 2 * x, which gives 9 = 2x.
Step 6: Divide both sides by 2 to find x: x = 9 / 2 = 4.5.
Step 7: Repeat steps 4-6 for the second side (4): (4 / y) = (2 / 3). Cross-multiply to get 4 * 3 = 2 * y, which gives 12 = 2y. Then, y = 12 / 2 = 6.
Step 8: Repeat steps 4-6 for the third side (5): (5 / z) = (2 / 3). Cross-multiply to get 5 * 3 = 2 * z, which gives 15 = 2z. Then, z = 15 / 2 = 7.5.
Step 9: The lengths of the corresponding sides of the second triangle are 4.5, 6, and 7.5.
Step 10: Round these values to the nearest whole numbers: 4.5 rounds to 6, 6 stays 6, and 7.5 rounds to 8.
