the perimeter of a rectangle is 182 inches the length exceeds the width by 59 inches find the length and the width
P = 2L + 2W
182 = 2(W + 59) + 2W
182 = 4W + 118
182 - 118 = 4W
64 = 4W
16 = W
To find the length and width of the rectangle, we can set up a system of equations based on the given information.
Let's assume:
Length = L
Width = W
We are given two pieces of information:
1. The perimeter of the rectangle is 182 inches, which can be expressed with the formula:
Perimeter = 2*(Length + Width)
2. The length exceeds the width by 59 inches, which can be expressed as:
Length = Width + 59
Now we can create the equations:
Equation 1: Perimeter = 2*(Length + Width)
182 = 2*(L + W) [Substituting the given value of the perimeter]
Equation 2: Length = Width + 59
L = W + 59 [Substituting the given relationship between length and width]
Now we can solve this system of equations to find the values of L and W:
Let's solve Equation 2 for W:
W = L - 59 [Rearranging Equation 2]
Now substitute this value of W in Equation 1:
182 = 2*(L + (L - 59)) [Substituting W = L - 59]
Simplifying:
182 = 2*(2L - 59) [Combining like terms]
Now, let's distribute the 2:
182 = 4L - 118 [Distributing the 2]
Next, isolate L by adding 118 to both sides:
182 + 118 = 4L
300 = 4L
Finally, divide both sides by 4 to solve for L:
L = 300 / 4
L = 75
Now substitute this value of L back into Equation 2 to find W:
W = L - 59
W = 75 - 59
W = 16
So, the length of the rectangle is 75 inches and the width is 16 inches.