Question

enter the scale terrell used to make the pattern of the kite.
2 in.
5 ft
set up a proportion to determine the base length, b, of the kite in feet.
scale (\frac{2 \text{ in.}}{5 \text{ ft}} = \frac{square \text{ in.}}{b \text{ ft}}) (leftarrow \frac{\text{base length of pattern}}{\text{base length of kite}})
b =
set up a proportion to determine the right side length, r, of the kite in feet.

Explanation:

Step1: Identify the pattern's base length

Assume the base length of the pattern (in inches) is needed. Wait, the problem's proportion is \(\frac{2\ \text{in.}}{5\ \text{ft}}=\frac{\text{base length of pattern (in)}}{b\ \text{ft}}\). But we need the pattern's base length. Wait, maybe the pattern's base length is given? Wait, the image might have the pattern's base length, but since it's not shown, maybe a typical problem: suppose the pattern's base length is, say, 6 inches (common problem). Wait, no, the user's image: maybe the pattern's base length is, for example, if the scale is 2 in. /5 ft, and the pattern's base is, say, 6 in. Then:

Step2: Set up proportion

Let the pattern's base length be \(x\) inches (from the pattern). Then \(\frac{2}{5}=\frac{x}{b}\), so \(b = \frac{5x}{2}\).

Wait, maybe the pattern's base length is 6 in (common problem). Then:

Step3: Solve for \(b\)

If \(x = 6\) in, then \(\frac{2}{5}=\frac{6}{b}\). Cross - multiply: \(2b=5\times6 = 30\), so \(b = 15\) ft.

But since the problem's image might have the pattern's base length, but assuming the pattern's base length is, for example, 6 in (common in such problems), the proportion is \(\frac{2}{5}=\frac{\text{pattern base (in)}}{b}\), and solving gives \(b\) as \(\frac{5\times\text{pattern base (in)}}{2}\).

Wait, the first part: the scale is \(2\) in. to \(5\) ft. Then, for the proportion, the numerator of the second fraction is the base length of the pattern (in inches), and the denominator is \(b\) (in feet). So if, say, the pattern's base length is 6 inches (from a typical problem), then:

\(\frac{2}{5}=\frac{6}{b}\)

Cross - multiply: \(2b = 5\times6=30\)

\(b=\frac{30}{2}=15\)

Answer:

For the proportion, the numerator (pattern base length in inches) depends on the pattern, but if we assume the pattern's base length is 6 inches (common), then \(b = 15\) ft. The scale is \(2\) inches to \(5\) feet, and the proportion is \(\frac{2}{5}=\frac{\text{pattern base (in)}}{b}\), with \(b=\frac{5\times\text{pattern base (in)}}{2}\).