Question

Mr. Thompson drew a rectangle on the chalkboard with a length to width ratio of 5 to 2. He asked students to draw a rectangle with the same ratio of length to width in their journals. Audrey plans to draw a rectangle with a width of 6 centimeters.
What length should Audrey's rectangle have?

Answer 1

To find the length of Audrey's rectangle based on the length to width ratio of 5 to 2, we start by noting that the ratio can be represented as:

\[
\frac{\text{length}}{\text{width}} = \frac{5}{2}
\]

Let the width of Audrey's rectangle be \( w = 6 \) centimeters. We can represent the length \( l \) in terms of this ratio:

\[
\frac{l}{6} = \frac{5}{2}
\]

Now, we can solve for the length \( l \) by cross-multiplying:

\[
l \cdot 2 = 5 \cdot 6
\]

This simplifies to:

\[
2l = 30
\]

Dividing both sides by 2 gives:

\[
l = 15
\]

Therefore, the length of Audrey's rectangle should be \( \boxed{15} \) centimeters.