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.
P = 2L + 2W
62 = 2(W + 7) + 2W
62 = 4W + 14
48 = 4w
12 = W
L=19
W=12
Let's assume the width of the rectangle is x inches.
According to the given information, the length of the rectangle is 7 inches longer than the width, so the length would be x + 7 inches.
The perimeter of a rectangle is given by the formula: perimeter = 2(length + width).
Substituting the given values, we have: 62 = 2(x + 7 + x).
Simplifying the equation, we get: 62 = 2(2x + 7).
Expanding and simplifying further, we have: 62 = 4x + 14.
Subtracting 14 from both sides of the equation, we get: 48 = 4x.
Dividing both sides by 4, we find that x = 12.
Therefore, the width of the rectangle is 12 inches and the length is 12 + 7 = 19 inches.
To find the measures of the length and width of the rectangle, we can use the information given in the problem.
Let's assume the width of the rectangle is "w" inches.
According to the problem, the length of the rectangle is 7 inches longer than the width. So, the length would be "w + 7" inches.
The formula for calculating the perimeter of a rectangle is:
Perimeter = 2(length + width)
Substituting the values from the problem into the formula:
62 = 2(w + 7 + w)
Now, we can simplify the equation and solve for "w":
62 = 2(2w + 7)
62 = 4w + 14
4w = 62 - 14
4w = 48
w = 48/4
w = 12
So, the width of the rectangle is 12 inches.
To find the length, we can substitute the value of "w" into the expression "w + 7":
Length = 12 + 7
Length = 19
Therefore, the length of the rectangle is 19 inches and the width is 12 inches.