Question

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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 bottom horizontal sides are 5 yd and 9 yd. Let the missing top side be \( x \). Since the figure has right angles, the total horizontal length on the bottom should equal the total horizontal length on the top. So, \( x = 5 + 9 \)? Wait, no, wait. Wait, the left vertical side is 16 yd, and the right part has a vertical side of 10 yd and 6 yd? Wait, no, let's look at vertical sides. Wait, the vertical length: the left side is 16 yd. The right part has a vertical segment of 10 yd and then 6 yd? Wait, no, the figure is a T - shape? Wait, no, let's think about horizontal sides. The bottom has two horizontal segments: 5 yd and 9 yd. The top horizontal segment is the missing one. Also, the vertical sides: the left side is 16 yd. The right part has a vertical side of 10 yd (the lower part) and 6 yd (the upper part). Wait, actually, for horizontal sides, the sum of the bottom horizontal segments (5 yd and 9 yd) should equal the top horizontal segment. Wait, no, wait, maybe I got it wrong. Wait, let's consider the horizontal direction. The bottom has a 5 yd segment and a 9 yd segment. The top horizontal side (the missing one) should be equal to 5 + 9? Wait, no, wait, let's check vertical. Wait, the left vertical side is 16 yd. The right part: the lower vertical segment is 10 yd, and the upper vertical segment is 6 yd. Wait, 10 + 6 = 16, which matches the left vertical side. Now for horizontal: the bottom has 5 yd, and the middle horizontal segment is 9 yd. So the top horizontal side (the missing one) should be 5 + 9? Wait, no, wait, the bottom horizontal is 5 yd, and the middle horizontal (the one above the 10 yd vertical) is 9 yd. So the top horizontal (the missing side) is 5 + 9? Wait, 5 + 9 = 14? Wait, no, wait, let's do it properly. In a rectilinear figure (all right angles), the sum of the lengths of the horizontal sides on the bottom is equal to the sum of the horizontal sides on the top. The bottom has two horizontal segments: 5 yd and 9 yd. So the top horizontal segment (the missing one) is 5 + 9 = 14? Wait, but let's check again. Wait, the left vertical side is 16 yd. The right vertical side is composed of 10 yd and 6 yd, 10 + 6 = 16, which is correct. Now for horizontal: the bottom horizontal length is 5 yd (the left part) and then the middle part is 9 yd (the part above the 10 yd vertical). So the top horizontal length (the missing side) is 5 + 9 = 14 yd? Wait, yes, because in the horizontal direction, the total length from left to right should be the same at the top and bottom. So 5 + 9 = 14.

Step2: Calculate the missing side

The missing side length \( x=5 + 9=14\) yards. Wait, let's confirm. The bottom horizontal: 5 yd (left) and 9 yd (right of the 5 yd). The top horizontal is the missing side, which should be equal to 5 + 9 = 14 yd. Yes, that makes sense because the figure is made of rectangles, so the horizontal lengths must match.

Answer:

14 yards