the difference between the length and width of a rectangle is 5 centimeters. what is the length(the longer side) of the rectangle, if the perimeter is equal to 66 centimeters
P = 2L + 2W
66 = 2(W + 5) + 2W
66 = 4W + 10
56 = 4W
14 = W
To find the length of the rectangle, we need to set up an equation based on the given information.
Let's assume the length of the rectangle is represented by "L" and the width is represented by "W".
According to the given information, the difference between the length and width is 5 centimeters, which can be expressed as:
L - W = 5 (Equation 1)
The formula for the perimeter of a rectangle is given by:
Perimeter = 2L + 2W
In this case, the perimeter is given as 66 centimeters. Substituting the known values in the formula, we get:
66 = 2L + 2W (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (L and W) that we can solve simultaneously to find the length of the rectangle.
One way to solve this system of equations is by substitution. Let's solve Equation 1 for L:
L = W + 5
Now substitute this value of L in Equation 2:
66 = 2(W + 5) + 2W
66 = 2W + 10 + 2W
66 = 4W + 10
Subtracting 10 from both sides:
56 = 4W
Dividing both sides by 4:
14 = W
Thus, the width of the rectangle is 14 centimeters.
To find the length, substitute the value of W back into Equation 1:
L - 14 = 5
Adding 14 to both sides:
L = 19
Therefore, the length of the rectangle is 19 centimeters.