Question

Ms. Kochhar drew a rectangle on the chalkboard with a length to width ratio of 5 to 3. She asked students to draw a rectangle with the same ratio of length to width in their journals. Drew plans to draw a rectangle with a width of 6 centimeters. What length should Drew's rectangle have?

Answer 1

Drew's rectangle should have a length of 10 centimeters.

Step-by-step explanation:

Ms. Kochhar provided a length to width ratio of 5 to 3 for the rectangle drawn on the chalkboard. This means that for every 5 units of length, there are 3 units of width. Given that Drew plans to draw a rectangle with a width of 6 centimeters, we can use the ratio to find the corresponding length.

To find the length, we can set up a proportion using the given ratio:

`\[ (5)/(3) = \frac{\text{Length}}{\text{Width}} \]`

Substituting the known values, where the width is 6 centimeters:

`\[ (5)/(3) = \frac{\text{Length}}{6} \]`

Cross-multiplying to solve for the length:

`\[ 5 * 6 = 3 * \text{Length} \]`

`\[ \text{Length} = (5 * 6)/(3) \]`

`\[ \text{Length} = 10 \]`

Therefore, Drew's rectangle should have a length of 10 centimeters to maintain the given ratio of 5 to 3.

In conclusion, by understanding the concept of ratios and setting up a proportion, we determined that the length of Drew's rectangle should be 10 centimeters.

This method allows for a straightforward and precise way to find the corresponding length when given a specific width-to-length ratio. It's a fundamental mathematical approach applicable in various real-life scenarios involving proportional relationships.