Question

find the missing side length. assume that all intersecting sides meet at right angles. include the correct unit in your answer. image of a composite rectangle with labeled sides: 12 ft (left side), 6 ft (top of left rectangle), 8 ft (right side of indent), 10 ft (bottom of right rectangle), 16 ft (bottom total length), and? (right side bottom length). unit options: in, ft, yd

Explanation:

Step1: Analyze vertical sides

The total vertical length is 12 ft. One part of the vertical side is 8 ft. Let the missing vertical side (the one we need to relate to find the horizontal missing side? Wait, no, actually, for the horizontal? Wait, no, the missing side is vertical? Wait, no, looking at the figure, the right - most vertical side is missing. Wait, let's think about the horizontal lengths first. The total horizontal length is 16 ft. The left - most horizontal segment is 6 ft, and the right - most horizontal segment is 10 ft. Wait, no, actually, for the vertical direction, the total height is 12 ft, and there is a segment of 8 ft. Wait, maybe we should look at the vertical and horizontal components.

Wait, the figure is a composite rectangle. Let's consider the vertical sides. The left - hand side is 12 ft. The vertical segment that is indented is 8 ft. So the remaining vertical length (the height of the lower rectangle) is \(12 - 8=4\) ft? Wait, no, maybe I got it wrong. Wait, let's look at the horizontal lengths. The total horizontal length is 16 ft. The first horizontal segment (top of the left rectangle) is 6 ft, and the horizontal segment to the right of the indent is 10 ft. Wait, \(6 + 10=16\), which matches the total horizontal length. Now for the vertical side: the left - hand side is 12 ft. The vertical segment that is part of the indent is 8 ft. So the missing vertical side (the right - most vertical side) should be \(12-8 = 4\) ft? Wait, no, wait. Let's think again. The figure has right angles, so the vertical sides: the left side is 12 ft. The vertical segment that is "cut out" has a length of 8 ft. So the remaining vertical length (the height of the lower part) is \(12 - 8=4\) ft. Wait, but the missing side is the vertical side on the right. Wait, no, maybe the missing side is horizontal? No, the question says "missing side length" and the figure has a vertical side with a "?". Wait, let's re - examine the figure.

The figure can be thought of as two rectangles: one on the left (6 ft wide and 12 ft tall) and a composite on the right. Wait, no, actually, the total height is 12 ft. The vertical segment that is 8 ft is part of the indent. So the height of the lower rectangle (the one with length 10 ft) is \(12 - 8 = 4\) ft. Wait, but the missing side is the vertical side? No, wait, maybe the missing side is the vertical side on the right. Wait, no, let's use the principle of rectangles: in a rectangle, opposite sides are equal.

Looking at the vertical directions: the left - hand vertical side is 12 ft. The vertical segment that is parallel to it and is indented is 8 ft. So the remaining vertical length (the height of the lower rectangle) is \(12-8 = 4\) ft. So the missing vertical side (the right - most vertical side) has a length of 4 ft. Wait, let's check with horizontal: the total horizontal length is 16 ft. The left horizontal segment is 6 ft, the right horizontal segment is 10 ft, and \(6 + 10=16\), which is correct. For the vertical: the left vertical is 12 ft, the indented vertical is 8 ft, so the missing vertical (the one at the bottom right) is \(12 - 8=4\) ft.

Step1: Calculate the difference in vertical lengths

The total vertical length (left - hand side) is 12 ft, and the vertical length of the indented part is 8 ft. To find the missing vertical side length, we subtract the indented vertical length from the total vertical length.
\[12-8 = 4\]

Answer:

4 ft