SOLUTION: A rectangle is to be drawn with perimeter 64cm. if the length is to be 14cm more than the width, determine the area of the rectangle

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Question 388668: A rectangle is to be drawn with perimeter 64cm. if the length is to be 14cm more than the width, determine the area of the rectangle
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter for a rectangle is 2L%2B2W=P where L is the length and W is the width. Since "A rectangle is to be drawn with perimeter 64cm", we know that P=64, which means that 2L%2B2W=64


Also since "the length is to be 14cm more than the width", we can say that L=W%2B14


So plug this into 2L%2B2W=64 to get 2%28W%2B14%29%2B2W=64


2W%2B28%2B2W=64 Distribute.


28%2B4W=64 Combine like terms on the left side.


4W=64-28 Subtract 28 from both sides.


4W=36 Combine like terms on the right side.


W=%2836%29%2F%284%29 Divide both sides by 4 to isolate W.


W=9 Reduce.


Since L=W%2B14 and W=9, this means that L=9%2B14=23


So L=23


So the length is 23 and the width is 9. This means that the area is A=LW=23%2A9=207


So the area is 207 square cm.



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