Question 942345: I need help on this following problem: The length of a rectangle measures 1 cm less than its width. The perimeter of the rectangle is 106 cm. Find the dimensions of the rectangle. Now i have tried to solve this problem in multiple attempts as can be seen here: 54+53=107, 53+52=105, 48+49=97, 50+49=99. Can you please help me solve this or solve it for me please!! Either choice is appreciated :)
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Guess-and-check is usually not the most efficient algorithm.
Also, the perimeter is twice the sum of length and width, i.e. P = 2(L+W).
Let W be the width, in cm. Its length is 1 cm less than the width, so L = W-1. Plugging in, we have 106 = 2((W-1)+W) = 2(2W-1) = 4W-2. Adding 2 to both sides, 108 = 4W. Dividing by 4, W = 27. The width is 27 cm and the length is 26 cm.
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