The first level of a dollhouse is in the shape of a rectangle. Its floor plan is shown in the following diagram.
Both the mudroom and the kitchen are square with areas of \(400\text{ cm}^2\) and \(2500\text{ cm}^2\), respectively. The living room is rectangular with an area of \(3000\text{ cm}^2\).
Determine the area of the rectangular storage room.
Let the width of a room be the vertical length of the room on the diagram. Let the length of a room be the horizontal length of the room on the diagram.
The kitchen is a square and has an area of \(2500\text{ cm}^2\). Its length and width must both be \(50\) cm since \(50\times 50=2500\text{ cm}^2\). The living room and kitchen have the same width. So the width of the living room must also be \(50\) cm. But the area of the living room is \(3000 \text{ cm}^2\), so the length of the living room is \(60\) cm since \(50\times 60=3000\text{ cm}^2\).
The mudroom is a square and has an area of \(400\text{ cm}^2\). Its length and width must both be \(20\) cm since \(20\times 20=400 \text{ cm}^2\). The mudroom and storage room have the same width. So the width of the storage room must also be \(20\) cm.
Now the length of the whole house can be calculated in two ways. We will equate these two expressions to find the length of the storage room. $$\begin{align} \text{mudroom length + storage room length} &= \text{living room length + kitchen length}\\ 20+\text{storage room length} &= 60+50\\ 20+\text{storage room length}&= 110\\ \text{storage room length}&= 90 \text{ cm} \end{align}$$
Since the width of the storage room is \(20\) cm and the length of the storage room is \(90\) cm, the area of the storage room is \(20\times 90=1800\text{ cm}^2\).