the widthe width of a rectangle is 6 inches less than the length. the perimeter is 72 inches. find the lengtj and the width
first represent unknowns using variables:
let x = length of rectangle
let x-6 = width of rectangle (according to first statement of problem)
now we set up equation,, since in the problem we are given the perimeter, we can use this to set up the equation,,
recall that perimeter of rectangle is
P = 2*(L+W)
where L is the length and W is the width
substituting,
72 = 2[ x + (x - 6) ]
we can divide both sides by 2 (to cancel 2 on the right side):
72/2 = x + x - 6
36 = 2x - 6
42 = 2x
x = 21 inches (length)
x-6 = 15 inches (width)
hope this helps~ :)
To solve this problem, let's assign variables to the length and width of the rectangle.
Let:
Length = L
Width = W
Given that the width of the rectangle is 6 inches less than the length, we can write the equation:
W = L - 6 (Equation 1)
The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since we have the formula for the perimeter, we can write another equation:
Perimeter = 2(L + W)
In this case, the given perimeter is 72 inches, so we have:
72 = 2(L + W) (Equation 2)
Now, let's substitute the value of W from Equation 1 into Equation 2:
72 = 2(L + L - 6)
72 = 2(2L - 6)
72 = 4L - 12
4L = 72 + 12
4L = 84
L = 84/4
L = 21
Substituting L back into Equation 1 to find the width:
W = 21 - 6
W = 15
Therefore, the length of the rectangle is 21 inches, and the width is 15 inches.
To find the length and width of the rectangle, we can set up an equation based on the given information.
Let's assume that the length of the rectangle is L inches.
According to the problem, the width of the rectangle is 6 inches less than the length. So, the width would be L - 6 inches.
The perimeter of a rectangle is the sum of all four sides. In this case, it is given that the perimeter is 72 inches.
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
Substituting the values we know:
72 = 2 * (L + (L - 6))
Now, we can simplify and solve for L:
72 = 2 * (2L - 6)
72 = 4L - 12
72 + 12 = 4L
84 = 4L
L = 84 / 4
L = 21
Therefore, the length of the rectangle is 21 inches.
To find the width, we can substitute the value of L into the equation for width:
Width = L - 6
Width = 21 - 6
Width = 15
Therefore, the width of the rectangle is 15 inches.
So, the length of the rectangle is 21 inches, and the width is 15 inches.