A rectangle is 12in longer than it is wide. The perimeter is 68m. Write an equation and show steps to find its length and width.
I need help figuring out what the equation would be. I found out that the length is 23 in and the width is 11 in, but I can't figure out how to make it into an equation.
P = 2L + 2W
68 = (2 * 23) + (2 * 11)
A rectangle is 12 in longer than it is wide mean:
L = W +12
Perimeter:
P = 2 L + 2 W = 2 ( L + W ) = 2 ( W + 12 + W ) = 2 ∙ ( 2 W + 12 )
P = 4 W + 24
68 = 4 W + 24
Subtract 24 to both sides
68 - 24 = 4 W + 24 - 24
44 = 4 W
Divide both sides by 4
44 / 4 = W
11 = W
W = 11 in
L = W +12 = 11 + 12 = 23 in
Thank you Bosnian
I also need to incorporate that the length is 12 more than the width into the equation, though.
To determine the equation for this problem, we need to use the given information. Let's start by assigning variables to the width and length of the rectangle.
Let's say the width of the rectangle is 'W' inches.
According to the problem, the rectangle is 12 inches longer than its width, so the length would be 'W + 12' inches.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.
Given that the perimeter of the rectangle is 68 inches, we can set up the equation:
68 = 2(W + 12) + 2W
Now, let's solve this equation to find the values of the width and length.
Step 1: Distribute 2 to the terms inside the parentheses.
68 = 2W + 24 + 2W
Step 2: Combine like terms.
68 = 4W + 24
Step 3: Move the constant term (24) to the right side by subtracting it from both sides.
68 - 24 = 4W
44 = 4W
Step 4: Divide both sides of the equation by 4 to isolate W.
44/4 = W
11 = W
So, the width of the rectangle is 11 inches.
To find the length, simply substitute the value of the width (11) into the expression W + 12:
Length = 11 + 12
Length = 23 inches
Therefore, the length of the rectangle is 23 inches, and the width is 11 inches.
The equation representing the problem is: 68 = 2(W + 12) + 2W.