The perimeter is the distance around a two-dimensional closed figure. One example is a rectangle. The lengths are on opposite parallel sides, and the widths are on opposite parallel sides. Both widths are equal, and both lengths are equal.
Suppose we abbreviate the lengths by the letter L, and the widths by the letter W. Here is a basic illustration:
W
________
L | _____| L
W
Thus, Perimeter = L + W + L + W
Let's abbreviate perimeter with the letter P.
The commutative law of addition tells us that x + y = y + x for any numbers x and y. Think about this: if you walk 3 miles and then walk 4 more, that's the same distance as walking 4 miles first and then 3 more.
So, P = L + W + L + W = L + L + W + W = 2L + 2W
= 2 ( L + W ).
Thus, P/2 = L + W, and in this case, P = 132 feet, so
132/2 = 66 = L + W
The problem tells us that
L = 6 more than 4 times W.
Converting this into an equation:
L = 6 + 4W.
Substituting this value into the previous equation,
66 = ( 6 + 4W ) + W = 6 + 5W
Subtracting 6 from both sides,
60 = 5W
And dividing both sides by 5,
12 = W.
L = 6 + 4W = 6 + 4*12 = 6 + 48 = 54.
Checking:
L + W + L + W = 54 + 12 + 54 + 12 = 132.
The checking part is NOT an option. It is easy to make a mistake. Checking makes sure we have found the correct answer.
