Question

The length of a rectangle is 5 more than its width. Find the length and the width of the rectangle if the ratio of the length to the width is at least 1.5 and no more than 3.

Answer 1

let l = length, w=width
first condition :
l = w+5 ---(1)
case1: \[l:w \ge 1.5\]\[(w+5) / w \ge 1.5\]\[w+5 \ge 1.5w\]\[w \le10\]\[l = w+5\]\[l-5\le10\]\[l \le15\]
case 2\[l:w \le3\]\[(w+5) / w \le3\]\[(w+5) \le3w\]\[ 5 \le2w\]\[w \ge 2.5\]
\[l = w+5\]\[l-5\ge2.5\]\[l \ge7.5\]
therefore \[2.5\le w \le10\] and \[7.5\le l \le15\]

Answer 2

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