6-mile perimeter. The length is 4 times the width.what is the length width
l =4w
P = 2l + 2w
6 = 2(4w) + 2w
6 = 8w + 2w
6 =10w
w = 6/10 = 3/5
l = 4w
l = 4(6/10)
l = 24/10 = 12/5
Well, if the perimeter is 6 miles, then maybe someone's been going round and round in circles! But let's get serious - let's solve this puzzle.
Let's call the width of our shape "w." Now, if the length is 4 times the width, we can call the length "4w."
To find the perimeter, we add up all the sides. For our shape, that would be 2w (the width) and 2(4w) (the length).
So, the perimeter equation would be 2w + 2(4w) = 6. Time for some math magic!
2w + 8w = 6
10w = 6
w = 6/10
w = 0.6 miles
Now that we know the width, we can find the length by multiplying it by 4.
Length = 4w = 4 * 0.6 = 2.4 miles
So, the length is 2.4 miles and the width is 0.6 miles. Voila!
Let's say the width of the shape is represented by "w". Since the length is 4 times the width, we can say the length is 4w.
To find the perimeter, we add up all the sides. In this case, we have two equal sides for the length and two equal sides for the width.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length) + 2(width)
Given that the perimeter is 6 miles, we can now set up the equation:
6 = 2(4w) + 2w
Simplifying the equation:
6 = 8w + 2w
Combining like terms:
6 = 10w
Now, we can solve for "w" by dividing both sides of the equation by 10:
6/10 = w
Simplifying:
0.6 = w
So, the width of the shape is 0.6 miles.
To find the length, you can substitute the value of "w" back into the equation:
Length = 4w
Length = 4(0.6)
Length = 2.4 miles
Therefore, the width is 0.6 miles and the length is 2.4 miles.
To find the length and width of a shape given the perimeter and a relationship between the length and width, we can set up a system of equations.
Let's denote the length as L and the width as W.
We are given two pieces of information:
1) The perimeter is 6 miles.
2) The length is 4 times the width. (L = 4W)
The perimeter of a shape is the sum of all its sides. In this case, we have two sides of length L and two sides of length W.
Therefore, we can set up the equation:
L + W + L + W = 6
Substituting the value of L from the second piece of information:
4W + W + 4W + W = 6
Simplifying the equation:
10W = 6
Dividing both sides by 10:
W = 0.6
Now that we have the width, we can substitute this value back into the equation for L:
L = 4W = 4(0.6) = 2.4
Therefore, the length is 2.4 miles and the width is 0.6 miles.