Val measures the perimeter of her rectangular garden as 80 ft. The width is 3x + 1 and the length is x – 5. What is the length and width in feet?
2(3x+1) + 2(x-5) = 50
Easy to solve, find x, sub back into width and length expressions
2 (3x+1) + 2 (x-5) = 80
3x+1 + x-5 = 40
4 x = 44
x = 11
w = 33+1 = 34
L = 6
Note, since the width is much more than the length I suspect a typo.
Damon, thanks for catching my copy error.
To find the length and width of Val's rectangular garden, we need to solve the given equation.
The formula for the perimeter of a rectangle is given by: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the perimeter is given as 80 ft, so:
80 = 2(l + w)
Now, we are given that the width (w) is represented as 3x + 1, and the length (l) is represented as x - 5.
Plugging these values into the equation, we get:
80 = 2((x - 5) + (3x + 1))
Next, we simplify the equation by combining like terms:
80 = 2(4x - 4)
Now, distribute the 2 to both terms inside the parentheses:
80 = 8x - 8
To isolate the variable, add 8 to both sides of the equation:
80 + 8 = 8x
88 = 8x
Finally, divide both sides of the equation by 8 to solve for x:
x = 11
Now that we have found the value of x, we can substitute it back into the expressions for the width and length to find their values.
The width is 3x + 1, so substituting x = 11:
Width = 3(11) + 1 = 33 + 1 = 34 ft
The length is x - 5, so substituting x = 11:
Length = 11 - 5 = 6 ft
Therefore, Val's rectangular garden has a width of 34 ft and a length of 6 ft.