Question

Which pairs of rectangles are similar polygons? Select Similar or Not Similar for each pair of rectangles. Similar Not Similar A and B Similar – A and B Not Similar – A and B B and C Similar – B and C Not Similar – B and C A and C Similar – A and C Not Similar – A and C Three rectangles labeled A, B, and C. The length of rectangle A is labeled as 150 centimeters and the width is labeled as 100 centimeters. The length of rectangle B is labeled as 108 centimeters and the width is labeled as 72 centimeters. The length of rectangle C is labeled as 132 centimeters and the width is labeled as 80 centimeters.

Answer 1

To determine if the rectangles are similar, we compare the ratios of their lengths to widths. A and B have the same ratio (1.5) and are similar; B and C have different ratios (1.5 and 1.65 respectively), as do A and C, so these pairs are not similar.

Step-by-step explanation:

To determine whether the pairs of rectangles are similar polygons, we need to compare the ratios of their corresponding sides. Rectangles are similar if the ratios of their lengths to their widths are the same.

• Rectangle A: 150 cm by 100 cm
• Rectangle B: 108 cm by 72 cm
• Rectangle C: 132 cm by 80 cm

For rectangles A and B, the ratio of the length to the width for rectangle A is 150/100 = 1.5. For rectangle B, this ratio is 108/72 = 1.5 as well. Since the ratios are equal, rectangles A and B are similar.

For rectangles B and C, the ratio for rectangle B is still 1.5, while for rectangle C, the ratio is 132/80 = 1.65. Because the ratios are not equal, rectangles B and C are not similar.

Finally, comparing rectangles A and C, A's ratio is 1.5 and C's ratio is 1.65, which are not equal. Hence, rectangles A and C are not similar.

We can conclude:

• A and B: Similar
• B and C: Not Similar
• A and C: Not Similar