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Math  /  Geometry

QuestionQuestion 9
Find the missing side length. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer. □\square ft ft2\mathrm{ft}^{2}

Studdy Solution

STEP 1

1. The shape is an L-shaped figure, which can be divided into two rectangles.
2. All intersecting sides meet at right angles.
3. The units for all lengths are in feet (ft).
4. We need to find the length of the missing side and ensure all lengths are consistent with the L-shaped figure.

STEP 2

1. Identify the overall dimensions of the L-shaped figure.
2. Break down the L-shaped figure into two rectangles.
3. Use the given lengths to find the unknown length by ensuring the dimensions match up.

STEP 3

Identify the total length and width of the L-shaped figure. The total vertical length is composed of the known lengths 16 ft and 7 ft.
Total vertical length=16 ft+7 ft=23 ft \text{Total vertical length} = 16 \text{ ft} + 7 \text{ ft} = 23 \text{ ft}

STEP 4

Identify the total horizontal length of the L-shaped figure. The total horizontal length is composed of the known lengths 13 ft and 9 ft.
Total horizontal length=13 ft+9 ft=22 ft \text{Total horizontal length} = 13 \text{ ft} + 9 \text{ ft} = 22 \text{ ft}

STEP 5

Break the L-shaped figure into two rectangles. Let’s denote the rectangles as Rectangle 1 and Rectangle 2. Rectangle 1 has dimensions 16 ft (vertical) and 13 ft (horizontal). Rectangle 2 has dimensions 7 ft (vertical) and an unknown horizontal side length.

STEP 6

Determine the missing side length by considering the total horizontal length. Since the total horizontal length is 22 ft and part of it is already known as 13 ft and 9 ft, we need to find the length that, when subtracted from 22 ft, gives us the remaining length.
Missing side length=22 ft−13 ft=9 ft \text{Missing side length} = 22 \text{ ft} - 13 \text{ ft} = 9 \text{ ft}

STEP 7

Check for consistency with the given lengths and the overall dimensions. The remaining side length should be consistent with the dimensions of the L-shaped figure.

STEP 8

Conclude that the missing side length is consistent with the given dimensions and thus is 9 ft.
Solution: The missing side length is 9 ft \boxed{9 \text{ ft}}

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