Comment The perimeter of any rectangle is P = 2L + 2W. It is customary to make the length (L) the longest side. That being said, the object is to set up a proportion and substitute that into the Perimeter formula.
Givens P = 42 cm W / L = 3/4
Set up the two equations from the givens. P = 2L + 2W = 42 W = 3/4 L
Step One Substitute the second equation into the first. 2L + 2(3/4)L = 42 Make an improper fraction of second term on the left. 2L + 6/4 L = 42 Reduce the fraction 2L + 3/2 L = 42 Multiply through by 2 4L + 3L = 84 Combine like terms. 7L = 84 Divide by 7 L = 84/7 L = 12
Step 2 Find the Width. 3/4 = W/12 Cross multiply 4W = 36 Divide by 4 W = 36/4 W = 9
