The perimeter of a rectangle is 34 ft. The length is 1 ft longer than the width. Find the dimensions. Write a system of linear equation and solve the resulting system. Let x be the length and y be the width.
2x+2y=
2x+2y=34
y+1=x
by substituting x you get
2(y+1)+2y=34
2y+2+2y=34
4y+2=34
4y=32
y=8
y+1=x
x=8+1=9
The system of linear equations can be written as follows:
1) Perimeter equation: 2x + 2y = 34
2) Length is 1 foot longer than the width: x = y + 1
To solve the system, we can use substitution or elimination method. Since the second equation already provides x in terms of y, we can use substitution.
Substitute x = y + 1 into the perimeter equation (equation 1):
2(y + 1) + 2y = 34
Simplify:
2y + 2 + 2y = 34
4y + 2 = 34
4y = 34 - 2
4y = 32
y = 32/4
y = 8
Now, substitute y = 8 back into the second equation to solve for x:
x = y + 1
x = 8 + 1
x = 9
So, the width of the rectangle is 8 ft and the length is 9 ft.
To find the system of linear equations, start by translating the given information into equations.
1) The perimeter of a rectangle is 34 ft. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Therefore, the equation for the perimeter is: 2l + 2w = 34.
2) The length is 1 ft longer than the width. In terms of the variables x and y (where x represents the length and y represents the width), this can be written as: x = y + 1.
So, the system of linear equations is:
Equation 1: 2x + 2y = 34
Equation 2: x = y + 1
To solve this system, we can use the method of substitution or elimination.
Using substitution:
In Equation 2, solve for x in terms of y: x = y + 1.
Substitute this expression for x into Equation 1:
2(y + 1) + 2y = 34
Distribute: 2y + 2 + 2y = 34
Combine like terms: 4y + 2 = 34
Subtract 2 from both sides: 4y = 32
Divide both sides by 4: y = 8
Substitute the value of y = 8 back into Equation 2 to solve for x:
x = y + 1
x = 8 + 1
x = 9
So, the dimensions of the rectangle are a length of 9 ft and a width of 8 ft.