0580/42 Feb/Mar 2022, Question 7: Area Factor of Similar Shapes
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks
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The question, in short
Solve four problems on similar picture frames: find a larger width from areas, bound a picture's area, recover a pre-sale frame price, and compare dollar and euro prices.
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Part (a) · 3 marks
Given areas 350 cm² and 1134 cm² of similar frames and smaller width 17.5 cm, calculate the larger frame's width.
- 1Area scale factor = 1134 ÷ 350 = 3.24
- 2Length scale factor = √3.24 = 1.8
- 3Width = 17.5 × 1.8 = 31.5 cm
Answer31.5
Part (b) · 2 marks
Picture length 15 cm and width 10.5 cm, each to nearest 5 mm; calculate the upper bound of its area.
- 1Upper bounds: 15 + 0.25 = 15.25 cm and 10.5 + 0.25 = 10.75 cm
- 2Upper bound of area = 15.25 × 10.75 = 163.9375 cm²
Answer163.9375 or 163 15/16
Part (c) · 2 marks
After an 18% reduction, 5 frames cost $166.05; calculate the original price of one frame.
- 1Sale price of one = 166.05 ÷ 5 = 33.21
- 2Original price = 33.21 ÷ 0.82 = $40.50
Answer40.50
Part (d) · 3 marks
Compare $57 with 48.20 euros at $1 = 0.88 euros; find the price difference in dollars and cents to the nearest cent.
- 148.20 euros = 48.20 ÷ 0.88 = $54.77…
- 2Difference = 57 − 54.77… = 2.227…
- 3= $2.23
Answer2.23
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