Final answer:
The value of x, when the width is 4x + 2 and the length is x + 4 with a perimeter of 52 ft for a rectangle, is 4.
Step-by-step explanation:
To find the value of x when given the perimeter of a rectangle, we can use the formula Perimeter = 2(Width + Length). Here, the width of the rectangle is 4x + 2 and the length is x + 4. The perimeter is given as 52 ft. Setting up the equation, we have:
2((4x + 2) + (x + 4)) = 52
Combine like terms and simplify:
2(5x + 6) = 52
Now, divide both sides by 2:
5x + 6 = 26
Subtract 6 from both sides:
5x = 20
Finally, divide both sides by 5 to solve for x:
x = 4
Therefore, the value of x is 4.