The perimeter of a rectangle is 18 ft.The length is 1 ft longer than the width. Find the deminsions using a system of linear equations.
width --- x
length -- x+1
solve for x ....
2x + 2(x+1) = 18
Let's represent the width of the rectangle as "w". According to the given information, the length of the rectangle is "1 ft longer than the width," which can be represented as "w + 1."
The perimeter of a rectangle can be calculated by adding the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter is given by the formula:
Perimeter = 2 * (length + width)
In this case, the perimeter is 18 ft. So we can set up the following equation:
18 = 2 * (w + (w + 1))
Simplifying the expression inside the parentheses:
18 = 2 * (2w + 1)
Now, let's solve this equation step-by-step to find the value of "w":
First, distribute the 2 on the right side of the equation:
18 = 4w + 2
Next, subtract 2 from both sides:
16 = 4w
Now, divide both sides by 4 to solve for "w":
w = 16 / 4
w = 4
Therefore, the width of the rectangle is 4 ft.
To find the length, substitute the value of "w" into the expression we found earlier:
Length = w + 1
Length = 4 + 1
Length = 5
Thus, the dimensions of the rectangle are:
Width = 4 ft
Length = 5 ft
To find the dimensions of the rectangle, we can set up a system of linear equations based on the given information.
Let's assume that the width of the rectangle is x ft.
Since the length is stated to be 1 ft longer than the width, we can express the length as (x + 1) ft.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
From the given information, we know that the perimeter is 18 ft. So we can set up the equation:
18 = 2[(x + 1) + x]
Simplifying this equation, we have:
18 = 2(2x + 1)
Now, let's solve this equation step by step to find the value of x (width), and subsequently, the value of (x + 1) (length):
First, distribute the 2 on the right side of the equation:
18 = 4x + 2
Next, subtract 2 from both sides of the equation:
18 - 2 = 4x + 2 - 2
16 = 4x
Now, divide both sides by 4 to isolate x:
16/4 = 4x/4
4 = x
So, the width of the rectangle is x = 4 ft.
To find the length, we can substitute the value of x in the expression (x + 1):
Length = 4 + 1 = 5 ft
Therefore, the dimensions of the rectangle are:
Width = 4 ft
Length = 5 ft