Perimeter, length, and width

Question

The perimeter P of a rectangle is P = 2l + 2w, where l and w are the rectangle’s length and width, respectively.
a) Rewrite the formula to find length given perimeter and width. Justify each step in your solution with the property used.

b)Compute the length of a rectangle with perimeter 40.2 in and width 6.7 in

Answer 1

a)

P = 2l + 2w   (subtract 2w from both sides)

P - 2w = 2l     (divide each side by 2)

(P - 2w)/2 = l   (split the numerator by using the common denominator)

P/2 - (2w)/2 = l     (simplify the fraction on left)

P/2 - w = l

 

b)

if P = 40.2 and w = 6.7

then we can solve for length using the formula derived in part a)

P/2 - w = l

40.2/2 - 6.7 = l

20.1 - 6.7 = l

13.4 = l

 

The length of the rectangle is 13.4 in when the perimeter is 40.2 in and width is 6.7 in.

 

Check:

P = 2(l + w) = 2(13.4 + 6.7) = 2(20.1) = 40.2