Question

try again
the value in your answer is incorrect.
find the missing side length.
assume that all intersecting sides meet at right angles.
include the correct unit in your answer.

Explanation:

Step1: Analyze horizontal sides

The total horizontal length is 16 ft. One horizontal segment is 9 ft, so the missing horizontal side (let's call it \( x \)) satisfies \( x + 9 = 16 \). Solving for \( x \), we get \( x = 16 - 9 = 7 \) ft.

Step2: Analyze vertical sides

The total vertical length can be found by adding the two vertical segments. One is 8 ft and the other is 5 ft, so total vertical length is \( 8 + 5 = 13 \) ft. Wait, but actually, for the vertical missing side (let's check again). Wait, the horizontal missing side is 7 ft (from step 1). Wait, maybe I misread. Wait, the figure is an L - shape. Let's re - examine. The bottom horizontal side is 16 ft. The right - most horizontal segment is 9 ft, so the left horizontal segment (the top of the left rectangle) is \( 16 - 9=7 \) ft. For the vertical side, the lower vertical segment is 5 ft, the upper vertical segment is 8 ft, so the total vertical side (the left - most side) is \( 8 + 5 = 13 \) ft? Wait, no, maybe the question is about the vertical side? Wait, the problem says "missing side length". Let's assume we need to find the left - most vertical side. The two vertical parts: 8 ft and 5 ft. So total vertical length is \( 8 + 5=13 \) ft? Wait, no, maybe the horizontal side. Wait, the top horizontal side: the bottom is 16 ft, the right horizontal part is 9 ft, so the left horizontal part (the top of the left rectangle) is \( 16 - 9 = 7 \) ft. Wait, maybe the vertical side: the left side. The lower part is 5 ft, the upper part is 8 ft, so total is \( 8 + 5=13 \) ft. Wait, let's check the units. The figure has units in ft. Let's re - do:

For horizontal sides: The bottom side is 16 ft. The right horizontal segment (the top of the right rectangle) is 9 ft. So the left horizontal segment (the top of the left rectangle) is \( 16 - 9=7 \) ft.

For vertical sides: The right vertical segment (the right side of the right rectangle) is 5 ft. The left vertical segment (the left side of the left rectangle) has an upper part of 8 ft and the lower part should be equal to the right vertical segment? No, wait, in a right - angled L - shape, the vertical length of the left part is equal to the sum of the vertical lengths of the right part? Wait, no. Let's think of the figure as two rectangles. One rectangle is on the left, with height \( h_1 \) and width \( w_1 \), and one on the right, with height \( h_2 = 5 \) ft and width \( w_2=9 \) ft. The total width is \( w_1 + w_2=16 \) ft, so \( w_1=16 - 9 = 7 \) ft. The total height of the left rectangle is \( h_1=8 + 5=13 \) ft? Wait, no, the right rectangle has height 5 ft, and the left rectangle has height 8 ft plus 5 ft? Wait, maybe the vertical side we need to find is the left - most side, which is \( 8 + 5 = 13 \) ft, and the horizontal side (the top of the left rectangle) is 7 ft. Wait, the problem says "missing side length". Let's check the figure again. The figure has a vertical segment of 8 ft, a vertical segment of 5 ft, a horizontal segment of 9 ft, and a horizontal segment of 16 ft. So the missing horizontal side (top left) is \( 16 - 9 = 7 \) ft, and the missing vertical side (left) is \( 8 + 5=13 \) ft. Wait, maybe the question is about the vertical side. Let's assume that. So the total vertical length is \( 8+5 = 13 \) ft.

Wait, maybe I made a mistake earlier. Let's start over. In a composite figure with right angles, the sum of the horizontal lengths on the top should equal the sum of the horizontal lengths on the bottom, and the sum of the vertical lengths on the left should equal the sum of the vertical lengths on the right.

Bottom horizontal length: 16 ft.

Top horizontal lengths: let the missing one be \( x \) and the other is 9 ft. So \( x + 9=16\Rightarrow x = 7 \) ft (horizontal missing side).

Right vertical length: 5 ft.

Left vertical lengths: 8 ft and the missing part (let's say \( y \)). So \( 8 + y=5 + \text{the other vertical part} \)? Wait, no, the left side is a single vertical side? Wait, no, the figure is L - shaped. So the left side has two parts? No, maybe the left side is a single vertical side with length equal to the sum of the two vertical segments on the right? Wait, the right has a vertical segment of 5 ft and the left has a vertical segment of 8 ft, so the total height (the left - most vertical side) is \( 8 + 5=13 \) ft. And the top - most horizontal side (the left part) is \( 16 - 9 = 7 \) ft.

Since the problem says "missing side length", and the units are ft. Let's assume we need to find the left - most vertical side. So the length is \( 8 + 5=13 \) ft. Or the top - most horizontal side is 7 ft. Wait, maybe the vertical side. Let's check the numbers again.

If we consider the vertical direction: the lower part is 5 ft, the upper part is 8 ft, so the total vertical length (the left side) is \( 8 + 5 = 13 \) ft.

Answer:

13 ft