the formula for finding the perimeter p of a rectangle with length l and width w is given. which formula shows how the length of a rectangle can be determined f

Question

Please help me I don't understand. The options are:

A. L = p/2 - 2w

B. L = p - 2w/2

C. L = p/2 + w

D. L = p -2/ 2w

Answer 1

P=2l+2w

P-2w=2l

(P-2w)/2=l

B. is the answer but it must have parentheses (  )

Answer 2

The perimeter of a rectangle is the sum of the lengths of all sides  : p = L + L + w + w

 

One half of the length of the perimeter is p/2, which would be the sum of L + w.

 

so p/2 = L + w 

 

To solve for L, subtract w from both sides, so p/2 - w = L

 

and if your write the equation with L on the left hand side, L = p/2 - w.

 

You will see problems like this often, using any formula you will be expected to solve for any variable.

 

Whenever possible, draw a picture. For this example draw a rectangle, then see how the sum of the length and width will be half of the perimeter.

 

P = L + L + w + w

P = 2L + 2w                     after you combine like terms

 

2L = P - 2w                    

Now divide both sides by 2 - every term on both sides

 

L = (p - 2w) /2    this could match choice B if there are parenthesis is the choice that are not shown above.