Find the missing side length. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer.

Steps to Solve

1. Identify the given dimensions

The figure contains several known side lengths:

• The vertical side on the left is 16 ft.
• The base of the figure has a length of 4 ft.
• From the vertical side in the middle, another vertical length is 6 ft.
• The horizontal side on top is 11 ft.
• Another vertical length is 7 ft.

2. Determine the total height of the figure

To find the total height of the figure, we sum the known vertical lengths:

• The total height is composed of the segments of 6 ft and 7 ft.

$$ \text{Total height} = 7 \text{ ft} + 6 \text{ ft} = 13 \text{ ft} $$

3. Calculate the missing length

The total height of the surrounding rectangle should equal the previously determined height plus the extension downwards: Since the left vertical side is 16 ft, we can find the missing length (denoted as $x$):

$$ x + 13 \text{ ft} = 16 \text{ ft} $$

4. Isolate the variable

To find $x$, subtract the total height from the length of the left vertical side:

$$ x = 16 \text{ ft} - 13 \text{ ft} = 3 \text{ ft} $$