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a + b = 8, a x b = 8 a = 8 - b so 8b - b^2 = 8 ie b^2 - 8b + 8 = 0 Using the quadratic formula gives (8 +/-sqrt(64 - 32)/2 ie (8 +/- 5.66)/2 = 4 +/- 2.83 so the dimensions are 1.17 and 6.83, which sum to 8 and multiply to 7.9911. Near enough?
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