The sides of a rectangle are in a 3:4 ratio. What is the length of the shorter sides of the rectangle if it's perimeter is 42cm

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

Check

P = 2L + 2W

2L + 2W = 42

2*12 + 2*9 = ? 42

24 + 18 = ? 42

42 = 42