A certain field is a rectangle with a perimeter of 858
feet. The length is 191
feet more than the width. Find the width and length of the rectangular field.
Let's start by using the formula for the perimeter of a rectangle: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We know the perimeter is 858, so we can write:
858 = 2L + 2W
Next, we know that the length is 191 feet more than the width. We can write:
L = W + 191
Now we can substitute L = W + 191 into the perimeter formula:
858 = 2(W + 191) + 2W
Simplifying this equation, we get:
858 = 4W + 382
Subtracting 382 from both sides, we get:
476 = 4W
Dividing both sides by 4, we get:
W = 119
Now that we know the width is 119 feet, we can use our equation for L in terms of W to find the length:
L = W + 191 = 119 + 191 = 310
Therefore, the width of the rectangular field is 119 feet and the length is 310 feet.
Let's let:
- x be the width of the rectangular field
- x + 191 be the length of the rectangular field
Since the perimeter of a rectangle is the sum of all its sides, we can set up the equation:
2(x + x + 191) = 858
Simplifying the equation:
2(2x + 191) = 858
4x + 382 = 858
4x = 858 - 382
4x = 476
x = 476/4
x = 119
So, the width of the rectangular field is 119 feet.
To find the length, we can substitute the value of x back into the equation:
Length = x + 191 = 119 + 191 = 310
Therefore, the width of the rectangular field is 119 feet and the length is 310 feet.