Area and Perimeter Unit Test

Question

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Question
Use the image to answer the question.

A composite shape is drawn, starting with a horizontally aligned rectangle. There is no measurement across the top, and the right side is labeled with a question mark. A horizontally aligned rectangular area marked as 8 feet in length and unknown in width is removed from the bottom left of the original rectangle. The remaining length on the right side is 2 feet. The remaining width on the left side is 3 feet. Corners are marked with right angles.

Tessa designs a supply closet as an addition to her house. The closet is pictured, and its total area is 36 square feet. What is the length in feet of the side of the supply closet labeled with the question mark?(1 point)
feet
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Answer 1

To find the length of the side of the supply closet labeled with the question mark, we can calculate based on the total area of the closet.

Let's denote the width of the removed rectangular area as \( W \).

From the description, the remaining width of the closet (on the left side) is 3 feet, and the remaining length (on the right side) is 2 feet. We can set up the total area of the shape with the following formula:

\[ \text{Area} = \text{Length} \times \text{Width} \]

Given that the total area of the supply closet is 36 square feet:

\[ \text{Area} = \text{Remaining Length} \times \text{Remaining Width} = 2 \text{ feet} \times (3 + W) \text{ feet} = 36 \text{ square feet} \]

This means:

\[ 2 \times (3 + W) = 36 \]

We can now solve for \( W \):

1. Divide both sides by 2:

\[ 3 + W = 18 \]

2. Subtract 3 from both sides:

\[ W = 15 \]

The dimension of the side of the closet labeled with the question mark is thus 15 feet.

So the answer is:

15 feet