Question

think about the process the blueprint of a concrete patio has a scale of 2 in. = 3 ft. you want to find the dimensions of a new blueprint of the patio with a scale of 4 in. = 5 ft. what is the first step in finding the dimensions with the new scale? find the dimensions with the new scale. the length of the blueprint with the new scale is \\( \square \\) in.

Explanation:

Step1: Find the actual length

Given the original scale \(2\) in \( = 3\) ft. Let the length on the original blueprint be \(l_{1}\) (assume \(l_{1}\) is not given in the problem, but if we assume the width is \(10\) in. For the length, if we assume the original - length - on - blueprint is \(x\) in. Using the scale \(2\) in \(=3\) ft, the actual length \(L\) (in feet) is \(L=\frac{3}{2}x\) ft. But if we assume the original - width - on - blueprint is \(10\) in, using the scale \(2\) in \( = 3\) ft, the actual width \(W\) (in feet) is \(W=\frac{3}{2}\times10 = 15\) ft.

Step2: Use the new scale

The new scale is \(4\) in \(=5\) ft. Let the new - length - on - blueprint be \(l_{2}\). We know that \(\frac{4}{5}=\frac{l_{2}}{L}\). Since \(L = 15\) ft (from the width calculation, assuming the length and width have the same actual - to - scale relationship). Then \(l_{2}=\frac{4\times15}{5}\)

$$l_{2}=\frac{4\times15}{5}=12$$

Answer:

\(12\)