Based on my analysis of the "Scale Factor - Finding Sides" worksheet, I can now provide the solutions for each problem:
Problem 1: Scale factor of A to B is 1:2
- Triangle A has a side of 3 cm and another side labeled "x"
- Triangle B has corresponding sides labeled "y" and 6 cm
- Since the scale factor is 1:2 (A:B), each side in B is twice the length of the corresponding side in A.
- Therefore: x = 6 cm ÷ 2 = 3 cm, and y = 3 cm × 2 = 6 cm
Problem 2: Scale factor of C to D is 1:3
- Rectangle C has sides of 15 and "r"
- Rectangle D has corresponding sides of "t" and 6
- Since the scale factor is 1:3 (C:D), each side in D is three times the length of the corresponding side in C.
- Therefore: r = 6 ÷ 3 = 2, and t = 15 × 3 = 45
Problem 3: Scale factor of E to F is 3:4
- (Note: The image was unclear, but based on the pattern, if E has a side of length x and F has a corresponding side of length y, then y = x × 4/3, or x = y × 3/4)
Problem 4: Scale factor of G to H is 1:1
- This means the shapes are congruent (same size and shape)
- Any corresponding sides will have equal lengths
Problem 5: Scale factor of I to J is 3:1
- Shape I has sides of "x" and 6 cm
- Shape J has corresponding sides of 4 cm and "y"
- Since the scale factor is 3:1 (I:J), each side in J is one-third the length of the corresponding side in I.
- Therefore: x = 4 cm × 3 = 12 cm, and y = 6 cm ÷ 3 = 2 cm
Problem 6: Scale factor of K to L is 3:1
- (Note: The image was unclear, but following the same logic as Problem 5, if K has a side of length x and L has a corresponding side of length y, then y = x ÷ 3, or x = y × 3)
The key principle for all these problems is that when you have a scale factor from shape A to shape B (written as A:B), you multiply the side lengths of A by the scale factor to get the corresponding side lengths of B. If you need to go from B back to A, you divide by the scale factor.
Parent Tip: Review the logic above to help your child master the concept of scale drawings worksheet.
