SOLUTION: The length of a rectangle is 4 centimeters less than its width. What are the dimensions of the rectangle if it’s area is 285 square centimeters.

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Question 1156142: The length of a rectangle is 4 centimeters less than its width. What are the dimensions of the rectangle if it’s area is 285 square centimeters.
Answer by jim_thompson5910(35256) (Show Source):
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Note that 285 ends with a 5, so we know that 5 is a factor by the divisibility rule for 5.
285/5 = 57
Then we see that the digits of 57 add to 5+7 = 12 which is a multiple of 3 (we can see that the digits of 12 add to 1+2 = 3 to help further show this point). Therefore, 57/3 = 19

When we do the full prime factorization for 285, we get
285 = 3*5*19
we can replace 3*5 with 15
285 = 15*19
note how 19 is 4 larger than 15
So we have shown a 15 by 19 rectangle yields an area of 285

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An algebraic approach

W = width
W-4 = length, since it is 4 cm less than the width
area = width*length
area =

area =

area = 285

Equate the two expressions and solve for W

Subtract 285 from both sides

Use the quadratic formula at this point. In this case, a = 1, b = -4, c = -285.

or

or

or

or

or

or

Ignore as a negative width is not possible.

The only practical solution is , so

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Answer: 15 cm by 19 cm