Kathy M. answered • 07/20/17

High School Math Teacher 9+years

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