Find the dimensions. The length is 200 feet more than the width, and the perimeter is 1,040 feet. Find the length and width, use the perimeter formula P= 2L +2W
The bot's solution is much too lengthy and cumbersome.
let the width be x ft
then the length = x+200 ft
2x + 2(x+200) = 1040
4x + 400 = 1040
4x = 640
x = 160
so the width is 160 ft, and the length is 360 ft
Let's use the given information to set up two equations.
1. "The length is 200 feet more than the width" can be written as:
L = W + 200
2. "the perimeter is 1,040 feet" can be written using the formula:
P = 2L + 2W
Substituting equation 1 into equation 2, we get:
P = 2(W + 200) + 2W
Simplifying the equation:
1,040 = 4W + 400
Subtracting 400 from both sides:
640 = 4W
Dividing both sides by 4:
W = 160
Now we can use equation 1 to find the length:
L = 160 + 200 = 360
Therefore, the dimensions of the rectangle are:
Width = 160 feet
Length = 360 feet