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length of rectangle is three feet more than the width. Its perimeter is 102. Find the length and width

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Given: Rectangle whose length is 3 feet more than its width and the perimeter of the rectangle is 102 feet.

 

Let P represent the variable for the perimeter. P=102 feet.

Let x represent the variable for the width.

From the given we know that the length of the rectangle is 3 feet more than the width.  This means that the length is equal to x+3.

 

The formula for the perimeter of a rectangle is

P=2(length)+2(width)

P=2(x+3)+2x

102=2x+6+2x

102=4x+6

96=4x

24=x

 

Since the width is the variable for x. We know that the width of the rectangle is 24 feet.

 

The length of the rectangle is the expression x+3.

Since the length=x+3, when we substitute 24 in for x, we know that the 

length=24+3=27 feet.

 

Final answer:

The length of the rectangle is 27 feet and the width is 24 feet. 

 

 

 

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