Question 571187
let L equal the length of your rectangle.
let W equal the width of your rectangle.
let P equal the perimeter of your rectangle.
the formula for the perimeter of a rectangle is 2L + 2W = P
since P equals 72, this formula becomes:
2L + 2W = 72
you are also given that L = 2W - 6
this equation says that the length of the rectangle is 6 inches less than twice the width.
you can substitute for L in the equation of:
2L + 2W = 72 to get:
2(2W-6) + 2W = 72
you simplify this equation to get:
4W - 12 + 2W = 72
you combine like terms to get:
6W - 12 = 72
you add 12 to both sides of this equation to get:
6W = 72 + 12
you combine like terms to get:
6W = 84
you divide both sides of this equation by 6 to get:
W = 84 / 6
you simplify this to get:
W = 14
since L = 2W - 6, this means that:
L = 2*14 - 6 which becomes:
L = 28 - 6 which becomes:
L = 22
you have:
L = 22 inches
W = 14 inches
going back to the original formula of:
2L + 2W = 72, you have:
2*22 + 2*14 = 72 which becomes:
44 + 28 = 72 which becomes:
72 = 72
this confirms the values for L and W are good.
your length is 22 inches.
your width is 14 inches.