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2012/13 AHSMC Part 1 Problem 9

Problem 9 of 16

A rectangle with integer length and width in cm has area 7070 cm2^2. Which of the following, in cm, cannot be the length of the perimeter of the rectangle?

Answer choices

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Solution

We have 70=1×70=2×35=5×14=7×1070 = 1 \times 70 = 2 \times 35 = 5 \times 14 = 7 \times 10. Thus there are four possible shapes of the rectangle, with respective perimeters 142142 cm, 7474 cm, 3838 cm and 3434 cm. The answer is (D).

University of Alberta