1. **Problem:** Find the scale factor of Figure B to Figure A given sides of triangles. Given sides: - Figure A: 36 and 25.2 - Figure B: 14 and 20 2. **Formula:** Scale factor from Figure B to Figure A is \( \frac{\text{side of B}}{\text{corresponding side of A}} \). 3. Calculate scale factors for both pairs: - \( \frac{14}{36} = \frac{7}{18} \approx 0.3889 \) - \( \frac{20}{25.2} = \frac{20}{25.2} \approx 0.7937 \) 4. Since scale factors must be consistent, check if any ratio matches given options. The ratio \( \frac{5}{9} \approx 0.5556 \) is between these values but not equal. 5. The closest consistent scale factor is \( \frac{5}{9} \) if sides correspond differently or rounded. --- 1. **Problem:** If the scale factor of Figure A to Figure B is 4:12, find \( x \). 2. **Formula:** \( \frac{x}{4} = \frac{24}{12} \) 3. Simplify right side: \( \frac{24}{12} = 2 \) 4. Solve for \( x \): \[ x = 4 \times 2 = 8 \] --- 1. **Problem:** Given \( \triangle KLJ \sim \triangle VWU \), find \( x \) using side ratios. 2. **Given:** \[ \frac{25}{20} = \frac{4x - 23}{2x + 2} \] 3. Cross multiply: \[ 25(2x + 2) = 20(4x - 23) \] 4. Expand: \[ 50x + 50 = 80x - 460 \] 5. Rearrange: \[ 50 + 460 = 80x - 50x \] \[ 510 = 30x \] 6. Solve for \( x \): \[ x = \frac{510}{30} = 17 \] **Final answers:** - Scale factor (B to A) approximately \( \frac{5}{9} \) - \( x = 8 \) for scale factor 4:12 - \( x = 17 \) for similar triangles \( \triangle KLJ \sim \triangle VWU \)