Question

The cheerleading squad is creating banners for an upcoming pep rally. The proportion of length to height for the banners must be 3 to 1.

Which graph represents this proportion?


W.
X.

Y.
Z.
A.
W
B.
X
C.
Z
D.
Y

Y dot: 4,9
Z dot: 3,9
X dot: 3,6
W dot: 3,9

Answer 1

To represent the proportion of length to height as 3 to 1, we can express this as an equation. If we denote length as \( L \) and height as \( H \), then the relationship can be written as:

\[
\frac{L}{H} = 3
\]

This can also be rearranged to show that:

\[
L = 3H
\]

For each of the given points, we'll evaluate them by checking if they satisfy this equation.

1. **Y dot: (4, 9)**
- Length = 4, Height = 9
- Check: \( 4 = 3 \times 9 \) → Not true (since \( 4 \neq 27 \))

2. **Z dot: (3, 9)**
- Length = 3, Height = 9
- Check: \( 3 = 3 \times 9 \) → Not true (since \( 3 \neq 27 \))

3. **X dot: (3, 6)**
- Length = 3, Height = 6
- Check: \( 3 = 3 \times 6 \) → Not true (since \( 3 \neq 18 \))

4. **W dot: (3, 9)**
- Length = 3, Height = 9
- Check: \( 3 = 3 \times 9 \) → Not true (since \( 3 \neq 27 \))

From the above checks, since none of the given points satisfy the proportion of 3 to 1, it seems there might be a misunderstanding in interpreting the question or the data provided.

Since we're actually looking for a graph that appropriately represents the ratio of length to height of 3 to 1, we can calculate the expected height based on the lengths of the dots given.

For a banner with a length of 3, the expected height according to the ratio would be:

\[
H = \frac{L}{3} = \frac{3}{3} = 1
\]

For a banner with a length of 4, the expected height is:

\[
H = \frac{4}{3} \approx 1.33
\]

For a banner with a length of 6, the expected height is:

\[
H = \frac{6}{3} = 2
\]

None of the points as they stand represents this exact ratio. Please reevaluate the data or clarity on dimensions required to further determine which may represent a ratio approaching 3 to 1 properly.