the length of a rectangle is 100 inches more than the width. if the perimeter of the rectangle is 1320 inches, find the dimensions
2x + 2(x+100) = 1320
Solve for x, then x+100.
Let's say the width of the rectangle is x inches.
According to the given information, the length of the rectangle is 100 inches more than the width. Therefore, the length would be x + 100 inches.
The perimeter of a rectangle is given by the equation: P = 2(length + width)
Substituting the values, we have: 1320 = 2(x + 100 + x)
Simplifying the equation, we get: 1320 = 4x + 200
Subtracting 200 from both sides, we have: 1120 = 4x
Dividing both sides by 4, we get: x = 280
So, the width of the rectangle is 280 inches.
The length can be found by adding 100 to the width: 280 + 100 = 380
Therefore, the dimensions of the rectangle are 280 inches (width) and 380 inches (length).
To find the dimensions of the rectangle, we can utilize the given information about the relationship between the length and the width.
Let's assume that the width of the rectangle is "W" inches. According to the problem, the length is 100 inches more than the width, so we can express the length as "W + 100" inches.
The perimeter of a rectangle is calculated by adding all the sides, which in this case is given as 1320 inches. The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Substituting the expressions for length and width into the formula, we get:
1320 = 2(W + 100 + W)
Simplifying the equation:
1320 = 2(2W + 100)
Dividing both sides of the equation by 2:
660 = 2W + 100
Subtracting 100 from both sides:
560 = 2W
Finally, dividing both sides by 2:
280 = W
Thus, the width of the rectangle is 280 inches.
Using this result, we can find the length by substituting the width value into the expression for the length:
Length = W + 100
Length = 280 + 100
Length = 380 inches
Therefore, the dimensions of the rectangle are:
Width = 280 inches
Length = 380 inches