The perimeter of a rectangle is 42 inches. If the width of the rectangle is 6 inches, what is the length? A.12 inches
B.15 inches
C.21 inches
D.40 inches

B. 15 inches.

Step-by-step explanation:

A rectangle shares two pairs of congruent opposite sides.

Perimeter = 42

Let:

the length of the rectangle = l

the width of the rectangle = w = 6

Perimeter = l + l + w + w

Plug in 42 for perimeter &  6 for w in the equation:

42 = l + l + 6 + 6

Combine like terms:

42 = ( l + l ) + (6 + 6)

42 = 2l + 12

Next, isolate the variable, l. Do the opposite of PEMDAS.  First, subtract 12 from both sides:

42 (-12) = 2l + 12 (-12)

42 - 12 = 2l

30 = 2l

Next, divide 2 from both sides:

(30)/2 = (2l)/2

l = 30/2

l = 15

B. 15 inches is the length of the rectangle.

Check:

l + l + w + w = 42

15 + 15 + 6 + 6 = 42

30 + 12 = 42

42 = 42 (True).

~

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.