Final answer:
To find the length of the rectangle, set up an equation using the given information. Solve the equation to find the width of the rectangle. Substitute the width back into the expression to find the length.
Step-by-step explanation:
To find the length of the rectangle, we need to set up an equation using the given information. Let's say the width of the rectangle is 'w'. The problem states that the length is 4 feet shorter than twice the width, so the length is 2w - 4. The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width. We can set up the equation 430 = 2((2w - 4) + w) and solve for 'w'.
Start by distributing the 2: 430 = 2(3w - 4) = 6w - 8. Now, add 8 to both sides to isolate the variable: 438 = 6w. Divide both sides by 6: w = 73. Thus, the width of the rectangle is 73 feet.
Finally, to find the length, substitute the width back into the expression for the length: l = 2w - 4 = 2(73) - 4 = 142. Therefore, the length of the rectangle is 142 feet.