To find the dimensions of the concrete patio with the new scale, the first step is to convert the dimensions from the old scale to actual dimensions. Since the old scale is 2 inches equals 3 feet, you need to get the actual dimensions from the scale drawing first.
Once you have the actual dimensions, you can then convert these to the new scale of 4 inches equals 5 feet.
Given that:
- The old scale is 2 in. = 3 ft.
- The new scale is 4 in. = 5 ft.
To find the actual dimensions from the scale drawing (which are provided as 28 in. for length and 26 in. for width), you should multiply by the ratio that takes you from drawing inches (2 in.) to actual feet (3 ft.).
So, the correct first step in finding the actual dimensions of the patio is:
B. Multiply each dimension on the scale drawing by \(\frac{3 ft}{2 in.}\) to find the actual dimension of the patio.
Now, let's calculate the actual dimensions based on the provided lengths:
-
For Length (28 in.): \[ \text{Actual Length} = 28 , \text{in.} \times \frac{3 , \text{ft}}{2 , \text{in.}} = 28 \times 1.5 = 42 , \text{ft} \]
-
For Width (26 in.): \[ \text{Actual Width} = 26 , \text{in.} \times \frac{3 , \text{ft}}{2 , \text{in.}} = 26 \times 1.5 = 39 , \text{ft} \]
Now, to express these actual dimensions in relation to the new scale, convert back to the new scale of 4 in. = 5 ft:
To convert from feet to inches using the new scale:
- For 5 ft = 4 in, we have: \[ 1 , \text{ft} = \frac{4 , \text{in.}}{5 , \text{ft}} = 0.8 , \text{in.} \]
Now, we'll convert the actual dimensions back into the new scale:
-
New Length in inches: \[ 42 , \text{ft} \times 0.8 , \text{in.} = 33.6 , \text{in.} \]
-
New Width in inches: \[ 39 , \text{ft} \times 0.8 , \text{in.} = 31.2 , \text{in.} \]
So, the dimensions of the new blueprint with the scale of 4 in. equals 5 ft would approximately be:
- Length = 33.6 inches
- Width = 31.2 inches
But the appropriate first step in the process is indeed Option B.