Question

Students were asked to write a formula for the length of a rectangle by using the formulafor its perimeter, p= 2l+ 2w. Three of their responses are shown below.I. L=1/2p-wII. L= 1/2 (p-2w)III. L=(p-2w)/2 Which responses are correct?1) I and II, only3) I and III, only2) II and III, only4)I, II, and III

Answer 1

Given the formula for the perimeter of a rectangle:

`p=2l+2w`

Where "p" is the perimeter, "l" is the length, and "w" is the width.

You can write a formula for the length of the rectangle by solving the given formula for "l":

1. Apply the Subtraction Property of Equality by subtracting this term from both sides of the equation:

`2w`

Then:

`p-(2w)=2l+2w-(2w)`

`p-2w=2l`

2. Apply the Division Property of Equality by dividing both sides of the equation by 2:

`(p-2w)/(2)=(2l)/(2)`
`l=(p-2w)/(2)`

3. You can rewrite the equation in this form:

`l=(1)/(2)(p-2w)`

Or you can rewrite it in the following form:

- Separate each numerator with the same denominator:

`(p)/(2)-(2w)/(2)=l`

- Simplify:

`l=(1)/(2)p-w`

Hence, the answer is: Option 4.