SOLUTION: Word problems are my Achilles heel in mathematics and I have a problem that is stumping me completely. Here is the question: In a rectangle, the perimeter is 54 feet. The width o

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Question 956337: Word problems are my Achilles heel in mathematics and I have a problem that is stumping me completely. Here is the question:
In a rectangle, the perimeter is 54 feet. The width of the rectangle is 3 feet more than the length. What are the length and width of the rectangle? Can you help me figure it out.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the formula for the perimeter of a rectangle is p = 2x + 2y, where:
x is the length
y is the width.
p is the perimeter.

since p = 56, the equation becomes:

56 = 2x + 2y

since the width of the rectangle is 3 feet more than the length, then:

y = x + 3

replace y with x + 3 to get:

56 = 2x + 2y becomes:

56 = 2x + 2*(x+3)

simplify to get:

56 = 2x + 2x + 6

combine like terms to get:

56 = 4x + 6

solve for x to get:

x = (56 - 6) / 4 which becomes:

x = 12.5

since y = x + 3, then y = 15.5

your formula of y = 2x + 2y becomes:

56 = 2 * 12.5 + 2 * 15.5 which becomes:

56 = 25 + 31 which becomes:

56 = 56

this confirms the solution is correct.

x represents the length so the length is 12.5

y represents the width so the width is 15.5

the choice of x to represent length and y to represent width is arbitrary.

any letter could have been used.

you could have said a = length and b = width.

you could have said L = length and W = width.

the result would have been the same.

the length is 12.5 and the width is 15.5.





Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Word problems are my Achilles heel in mathematics and I have a problem that is stumping me completely. Here is the question:
In a rectangle, the perimeter is 54 feet. The width of the rectangle is 3 feet more than the length. What are the length and width of the rectangle? Can you help me figure it out. 
Let the length be L, and width, W

Then 2L + 2W = 54______2(L + W) = 2(27)______L + W = 27 -------- eq (i)

Also, W = L + 3 ------ eq (ii)

L + L + 3 = 27 ------- Substituting L + 3 for W in eq (i)

2L + 3 = 27

2L = 24

L, or length = , or  ft

Width = 12 + 3, or  ft 

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