Answer: The length is 31 inches and the width is 9 inches
Step-by-step explanation: The first clue we have is that the length is given as 4 inches more than three times the width. So if the width is W, then the length would be three times W and then add four to it. Hence, the length would be,
3W + 4
Therefore Length = 3W + 4 and Width = W
If the perimeter has been given as 80 inches, we can now apply the formulae for perimeter of a rectangle.
Perimeter = 2(L + W)
(Having determined the values of Length and Width...)
Perimeter = 2(3W + 4 + W)
Perimeter = 2(4W + 4)
Perimeter = 8W + 8
Having been given the perimeter as 80,
80 = 8W + 8
Subtract 8 from both sides of the equation
72 = 8W
Divide both sides of the equation by 8
9 = W
Having calculated the width as 9 inches, the length given as 3W + 4 now becomes
L = 3(9) + 4
L = 27 + 4
L = 31
Therefore length = 31 inches and width = 9 inches
