good morning Carol,
The perimeter of the rectangle is found by adding up all the sides of the rectangle.
Perimeter = length + width + length + width
introducing the variables as follows P = perimeter, L = length, W = width
then we have the equation P = L + W + L + W
however, we are told that "the length of the rectangle is 5 inches less than twice its width"
which converts into L = 2W - 5
we also are given the fact that the perimeter is 26 inches
which converts into P = 26
replacing all this information into our equation P = L + W + L + W
we get the following 26 = 2W - 5 + W + 2W - 5 + W
simplifying 26 = 6W - 10
isolating W on one side by adding 10 on both sides 26 + 10 = 6W - 10 + 10
simplifying 36 = 6W
dividing both sides by 6 36 / 6 = 6W / 6
we get 6 = W or the more familiar notation W = 6
substituting this obtained value of width , W = 6, into the equation for the length L = 2W - 5
we get the following L = 2 (6) - 5
= 12 - 5
= 7
so the rectangle has a width of W = 6 and a length of L = 7
checking the solution: P = L + W + L + W
= 7 + 6 + 7 + 6
= 26
