SOLUTION: The width of a rectangle is one half the length minus 11 cm. The area of the rectangle is 700 square centimeters. find the length and width.

Question 1067256: The width of a rectangle is one half the length minus 11 cm. The area of the rectangle is 700 square centimeters. find the length and width.
Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
length = x

(x/2 - 11)(x) = 700
x^2/2 - 11x - 700 = 0
x^2 - 22x - 1400 = 0
(x - 50)(x + 28) = 0

The length is 50 cm and the width is 14 cm.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Opening comment....

The wording is poor; we don't know for sure whether "the width is one half the length minus 11" means the width is or .

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Note the formal algebraic solution, as shown by the other tutor, requires you to solve the equation to find the answer to the problem. You of course can always solve a quadratic equation by using the quadratic formula; but without that you have to factor that quadratic, and the factorization is not easy with the large numbers.

So the formal algebra doesn't get you any closer to the solution. If a formal algebraic solution is not required, you might as well solve the problem informally, by trial and error.

You know the width is less than half the length; and you know the product of length and width is 700. So look for two numbers with a product of 700 in which one of the numbers is 11 less than half the other.

20*35 no; 20 is more than half of 35
10*70 no; 10 is less than half of 70, but it is not 11 less than half of 70
14*50 YES! 14 is less than half of 50, and 50/2-11=25-11=14

ANSWER: The width and length are 14 and 50.

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