Similar Figures

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Similar Figures · Grade 7 · Worksheet 2

1. Two similar triangles have corresponding sides in the ratio 2:5. If the perimeter of the smaller triangle is 48 cm, what is the perimeter of the larger triangle? Answer: 120 Solution: The ratio of corresponding sides is 2:5, so the scale factor from the smaller to the larger triangle is 5/2. The perimeter of the smaller triangle is 48 cm.
   Full step-by-step solution

   Step 1: The ratio of corresponding sides is 2:5, so the scale factor from the smaller to the larger triangle is 5/2. Step 2: The perimeter of the smaller triangle is 48 cm. Step 3: Multiply the smaller perimeter by the scale factor: 48 × (5/2) = 48 × 2.5 = 120. Step 4: The perimeter of the larger triangle is 120 cm. The answer is 120.

2. A scale drawing of a rectangular swimming pool has dimensions 4 cm × 6 cm. If the scale is 1:250, what is the actual area of the pool in square meters? Answer: 150 Solution: Drawing length = 6 cm Scale = 1:250 means 1 cm on drawing = 250 cm in reality Actual length = 6 cm × 250 = 1500 cm Drawing width = 4 cm Actual width = 4 cm × 250 = 1000 cm Actual length = 1500 cm ÷ 100 = 15 m Actual width = 1000 cm ÷ 100 = 10 m Area = length × width = 15 m × 10 m = 150 m² The…
   Full step-by-step solution

   Step 1: Convert the length from drawing to actual size Drawing length = 6 cm Scale = 1:250 means 1 cm on drawing = 250 cm in reality Actual length = 6 cm × 250 = 1500 cm Step 2: Convert the width from drawing to actual size Drawing width = 4 cm Actual width = 4 cm × 250 = 1000 cm Step 3: Convert centimeters to meters Actual length = 1500 cm ÷ 100 = 15 m Actual width = 1000 cm ÷ 100 = 10 m Step 4: Calculate the actual area Area = length × width = 15 m × 10 m = 150 m² The answer is 150.

3. Two similar rectangles have corresponding sides in the ratio 4:7. The smaller rectangle has a side length of 12 cm. What is the length of the corresponding side in the larger rectangle? Answer: 21 Solution: The ratio of corresponding sides is 4:7, meaning the scale factor from smaller to larger is 7/4. Let x be the length of the corresponding side in the larger rectangle.
   Full step-by-step solution

   Step 1: The ratio of corresponding sides is 4:7, meaning the scale factor from smaller to larger is 7/4. Step 2: Let x be the length of the corresponding side in the larger rectangle. Step 3: Set up the proportion: 4/7 = 12/x Step 4: Cross multiply: 4x = 7 × 12 Step 5: Calculate: 4x = 84 Step 6: Divide both sides by 4: x = 84 ÷ 4 = 21 Step 7: The corresponding side in the larger rectangle is 21 cm. The answer is 21.

4. A scale drawing of a rectangular swimming pool has dimensions 6 cm × 10 cm. If the scale is 1:150, what is the actual area of the pool in square meters? Answer: 135 Solution: Find the actual length using the scale factor 1:150 Actual length = 10 cm × 150 = 1500 cm Convert to meters: 1500 cm ÷ 100 = 15 m Find the actual width using the scale factor 1:150 Actual width = 6 cm × 150 = 900 cm Convert to meters: 900 cm ÷ 100 = 9 m Area = length × width = 15 m × 9 m = 135…
   Full step-by-step solution

   Step 1: Find the actual length using the scale factor 1:150 Actual length = 10 cm × 150 = 1500 cm Convert to meters: 1500 cm ÷ 100 = 15 m Step 2: Find the actual width using the scale factor 1:150 Actual width = 6 cm × 150 = 900 cm Convert to meters: 900 cm ÷ 100 = 9 m Step 3: Calculate the actual area Area = length × width = 15 m × 9 m = 135 m² The actual area of the swimming pool is 135 square meters.

5. Two similar rectangles have corresponding sides in the ratio 7:12. If the perimeter of the smaller rectangle is 42 cm, what is the perimeter of the larger rectangle? Answer: 72 Solution: The ratio of corresponding sides is 7:12, so the scale factor from the smaller to the larger is 12/7. For similar figures, the ratio of perimeters equals the ratio of corresponding side lengths.
   Full step-by-step solution

   Step 1: The ratio of corresponding sides is 7:12, so the scale factor from the smaller to the larger is 12/7. Step 2: For similar figures, the ratio of perimeters equals the ratio of corresponding side lengths. Step 3: Let P be the perimeter of the larger rectangle. Then 42/P = 7/12. Step 4: Cross multiply: 42 × 12 = 7 × P Step 5: 504 = 7P Step 6: Divide both sides by 7: P = 504 ÷ 7 = 72 The answer is 72.

6. A scale model of a rectangular swimming pool uses a scale of 1:150. On the model, the pool measures 12 cm by 8 cm. A similar rectangular hot tub is placed next to the pool. On the same model, the hot tub measures 3 cm by 2 cm. What is the actual area, in square meters, of the hot tub? Answer: 13.5 Solution: Identify the scale factor. The model uses a scale of 1:150, meaning 1 cm on the model represents 150 cm in reality. Convert the scale to meters.
   Full step-by-step solution

   Step 1: Identify the scale factor. The model uses a scale of 1:150, meaning 1 cm on the model represents 150 cm in reality. Step 2: Convert the scale to meters. Since 150 cm = 1.5 m, 1 cm on the model represents 1.5 m in reality. Step 3: Find the actual dimensions of the hot tub. Length: 3 cm × 1.5 m/cm = 4.5 m. Width: 2 cm × 1.5 m/cm = 3 m. Step 4: Calculate the actual area. Area = length × width = 4.5 m × 3 m = 13.5 square meters. The answer is 13.5.

7. Two similar rectangles have corresponding side lengths 7 cm and 21 cm. If the shorter side of the smaller rectangle is 7 cm, what is the length of the corresponding shorter side of the larger rectangle? Answer: 21 Solution: Identify the scale factor from the smaller rectangle to the larger rectangle using the given corresponding sides: 7 cm and 21 cm. Scale factor = 21 ÷ 7 = 3. Step 2: The shorter side of the smaller rectangle is 7 cm.
   Full step-by-step solution

   Step 1: Identify the scale factor from the smaller rectangle to the larger rectangle using the given corresponding sides: 7 cm and 21 cm. Scale factor = 21 ÷ 7 = 3. Step 2: The shorter side of the smaller rectangle is 7 cm. Multiply by the scale factor: 7 × 3 = 21 cm. The answer is 21.