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:

$\frac{p-2w}{2}=\frac{2l}{2}$$l=\frac{p-2w}{2}$

3. You can rewrite the equation in this form:

$l=\frac{1}{2}(p-2w)$

Or you can rewrite it in the following form:

- Separate each numerator with the same denominator:

$\frac{p}{2}-\frac{2w}{2}=l$

- Simplify:

$l=\frac{1}{2}p-w$

Hence, the answer is: Option 4.