Val measures the perimeter of her rectangular garden as 52 ft. The width is 2x - 1 and the length is x + 3.
What is the length and width in feet?
52 = 2 (2x - 1 + x + 3)
52 = 4x - 2 + 2x + 6
52 - 4 = 6x
48 = 6x
8 = x
Substitute 8 for x in your original problem.
To find the length and width of the rectangular garden, we need to solve for the values of x. Given that the perimeter is 52 ft, we can write the equation:
2(length + width) = perimeter
Substituting the given expressions for the length and width:
2((x + 3) + (2x - 1)) = 52
Simplifying the expression:
2(3x + 2) = 52
Now we can distribute the 2:
6x + 4 = 52
Next, we isolate the variable by subtracting 4 from both sides of the equation:
6x = 48
Finally, we solve for x by dividing both sides of the equation by 6:
x = 8
Now that we have the value of x, we can substitute it back into the expressions for the length and width:
Width = 2x - 1 = 2(8) - 1 = 15 ft
Length = x + 3 = 8 + 3 = 11 ft
Therefore, the width of the garden is 15 ft and the length is 11 ft.