Think About the Process The blueprint of a concrete patio has a scale of 2 in. equals 3 ft. You want to find the dimensions of a new blueprint of the patio with a scale of 4 in.equals5 ft. What is the first step in finding the dimensions with the new​ scale? Find the dimensions with the new scale.

Question

length
width
16 in.
14 in.
Question content area bottom
Part 1
What is the first step in finding the dimensions of the new​ scale?
A.
Multiply each dimension on the scale drawing by StartFraction 2 in. Over 3 ft EndFraction
to find the actual dimension of the patio.
B.
Multiply each dimension on the scale drawing by StartFraction 3 ft Over 2 in. EndFraction
to find the actual dimension of the patio.
C.
Multiply each dimension on the scale drawing by StartFraction 5 ft Over 4 in. EndFraction
to find the actual dimension of the patio.

Answer 1

To find the actual dimensions of the patio from the blueprint, you want to first find the scale conversion from the current blueprint to the actual dimensions.

Given that the original blueprint scale is \(2 \text{ in.} = 3 \text{ ft}\), you first need to find the actual dimensions using this scale. The relationship can be expressed as:

• \(1 \text{ in.} = \frac{3 \text{ ft}}{2} = 1.5 \text{ ft}\)

Therefore, to find the actual dimensions, you multiply the blueprint dimensions by:

• \( \frac{3 \text{ ft}}{2 \text{ in.}}\)

Next, you're looking to convert those actual dimensions to the new scale of \(4 \text{ in.} = 5 \text{ ft}\).

To find the actual dimensions with respect to the new scale, you should use the conversion of that new scale, which can be expressed as:

• \(1 \text{ in.} = \frac{5 \text{ ft}}{4}\)

So, your first step from your options would be:

B. Multiply each dimension on the scale drawing by \(\frac{3 \text{ ft}}{2 \text{ in.}}\) to find the actual dimension of the patio.

After you find the actual dimensions, you then use the new scale to express those dimensions in terms of the new blueprint.

To find the dimensions in the new scale (for the dimensions you provided: 16 in. and 14 in.), you would perform the following calculations for the actual dimensions:

1. For the length:

   • \( \text{Actual Length} = 16 \text{ in.} \times \frac{3 \text{ ft}}{2 \text{ in.}} = 24 \text{ ft}\)

2. For the width:

   • \( \text{Actual Width} = 14 \text{ in.} \times \frac{3 \text{ ft}}{2 \text{ in.}} = 21 \text{ ft}\)

Finally, to convert these actual dimensions back into dimensions using the new scale of \(4 \text{ in.} = 5 \text{ ft}\):

1. For the new length in inches:

   • \( \text{New Length} = 24 \text{ ft} \times \frac{4 \text{ in.}}{5 \text{ ft}} = 19.2 \text{ in.} \)

2. For the new width in inches:

   • \( \text{New Width} = 21 \text{ ft} \times \frac{4 \text{ in.}}{5 \text{ ft}} = 16.8 \text{ in.} \)

So, the new dimensions using the new scale would approximately be:

• Length: \(19.2 \text{ in.}\)
• Width: \(16.8 \text{ in.}\)

Make sure to round as necessary for your final dimensions!