Rectangle Dimensions The length of a rectangle is 7 inches longer than the width. If the perimeter of the rectangle is 62 inches, find the measures of the length and width.
L = 7 + W
P = 2L + 2W
62 = 2(7+w) + 2w
To find the measures of the length and width of a rectangle, we can set up an equation based on the information given.
Let's denote the width of the rectangle as "w" inches.
According to the problem, the length of the rectangle is 7 inches longer than the width, so the length can be represented as "w + 7" inches.
The formula for the perimeter of a rectangle is P = 2(length + width).
We are given that the perimeter of the rectangle is 62 inches. Substituting the length and width into the formula, we can set up an equation:
62 = 2(w + 7 + w)
Simplifying, we have:
62 = 2(2w + 7)
62 = 4w + 14
Rearranging the equation, we get:
4w = 62 - 14
4w = 48
Dividing both sides of the equation by 4, we find:
w = 12
Finally, substituting the value of w back into the expression for the length, we get:
Length = w + 7 = 12 + 7 = 19
Therefore, the width of the rectangle is 12 inches and the length is 19 inches.