Examples of Math Problems: The perimeter of a rectange is 54 centimeters, and its area is 140 square centimeters. Find the dimensions of the rectangle.

Monday, May 13, 2013

The perimeter of a rectange is 54 centimeters, and its area is 140 square centimeters. Find the dimensions of the rectangle.

%0D%0AP=2%28l%2Bw%29%0D%0A

becomes

%0D%0A54=2%28l%2Bw%29%0D%0A

or

%0D%0Al=27-w%0D%0A

and

%0D%0AA=lw%0D%0A

becomes

%0D%0Alw=140%0D%0A

then

%0D%0A%2827-w%29w=140%0D%0A

expanding and rewriting...

%0D%0Aw%5E2-27w%2B140=0%0D%0A

%0D%0Aw%5E2-27w%2B140=0%0D%0A

and the equation factors to
%0D%0A%28w-20%29%28w-7%29=0%0D%0A

%0D%0A%28w-20%29%28w-7%29=0%0D%0A

This means that w=20 and l=7

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