the primeter of a rectangle is 24ft. the length is 2 ft longer than the width. Find the dimensions. Write a system of linear equations and solve the resulting system. Let x be the length and y be the width,

write the first equation.
2x+2y=__
write the second equation.
x=y+__

what is the length?

what is the with?

Please help!!

x = length

y = width

Perimeter = 2x+2y
24 = 2x+2y

x = y + 2 Since the length is two feet longer than the width.

Use substitution to solve:

2(y+2) +2y = 24

okay. I came up with 14ft for the length and 10ft for the width.

correction length is 8ft and width is 4 ft.

0.34x

To solve this problem, we will write a system of linear equations based on the given information and then solve it.

Let's start with the first equation:
The equation for the perimeter of a rectangle is given by:
2(length + width) = perimeter
In this case, the perimeter is given as 24ft, so we can substitute it into the equation:
2(x + y) = 24
Now, let's simplify this equation:
2x + 2y = 24

Moving on to the second equation:
The problem states that the length (x) is 2ft longer than the width (y). This can be written as:
x = y + 2

Therefore, the system of linear equations becomes:
1) 2x + 2y = 24
2) x = y + 2

To solve the resulting system, we can use the substitution method, where we solve one equation for one variable and substitute that value into the other equation.

From equation 2), we have x = y + 2.
We can substitute this value for x in equation 1):
2(y + 2) + 2y = 24
2y + 4 + 2y = 24
4y + 4 = 24
4y = 20
y = 5

Now that we have the value of y, we can substitute it back into equation 2) to find x:
x = 5 + 2
x = 7

Therefore, the length (x) of the rectangle is 7ft, and the width (y) is 5ft.