Book Maths Puzzle Percentage

The width of a rectangle is 45% of the length. If the perimeter of the rectangle is 58cm, find its width.

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what the freak is the l.c.m AND the g.c.d. of 82, 96 and 112? i'm too tired to try this any more!
Thanks! To reach a damsell in distress, a knight places a 13-foot ladder against the castle wall. The base of the ladder is 7 feet less than the distance from the top of the ladder to the ground. How high on the castle will the ladder reach?