SOLUTION: The length of a rectangle is 14 m longer than its width and the area of the rectangle is 400 m2. Find the exact dimensions of the rectangle.

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Question 1143612: The length of a rectangle is 14 m longer than its width and the area of the rectangle is 400 m2. Find the exact dimensions of the rectangle.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!





That's not going to factor to give rational numbers.

Use the quadratic formula to get an exact answer in radical form, or a graphing calculator to get a decimal approximation.
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Let y be the value exactly half-way between the length and the width.


Then the length = y+7.  while the width = y-7.


The area is the product of length and width, i.e. (y+7)*(y-7) = .


Then the area equation is 


     = 400,


which implies


     = 400 + 49 = 449,

    y = .


Thus the length =  + 7 = 28.190 (approximately, with 3 right decimal places).    ANSWER

and  the width  =   - 7 = 14.190 (approximately, with 3 right decimal places).    ANSWER


CHECK.  The product of   + 7  and   - 7  is  400 = 449-49,  and the difference is 14, obviously.

Solved.

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Surely, this method is the same as to solve the problem using the quadratic formula, and it gives the same answer.

Its advantage is in that it is not so boring . . .


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To see many other problems solved by the similar method, look into the lessons
    - HOW TO solve the problem on quadratic equation mentally and avoid boring calculations
    - Three methods to find the dimensions of a rectangle when its perimeter and the area are given
    - Three methods to find the dimensions of a rectangle when its area and the difference of two dimensions are given
in this site.



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