fractions and lengths

Question

The width of a rectangle is 1/4 of the length. If you add 12 m to the width and double the length the perimeter is 120m. Determine the demensions of the orignal rectangle. 

Answer 1

P = 2L + 2w (rectangle perimeter formula)

L = 4w (length is 4 times as much as width)

120 =  2(12 + w) + 2(2L) (add 12 to width, double length, and the perimeter is 120 meters)

 

Okay, I'm dividing both sides by 2 right now:

120 / 2 =  (2(12 + w) + 2(2L)) / 2

60 = 12 + w + 2L

Alright. We have a value for L so plug it in:

60 = 12 + w + 2 * 4w

60 = 12 + w + 8w

Simplify:

60 = 12 + 9w

 

Subtract 12 from both sides:

60 - 12 = 12 + 9w - 12

48 = 9w

Divide by 9:

w= ⁴⁸/₉ → ¹⁶/₃

Now to find length:

L = ¹⁶/₃ * 4 = ⁶⁴/₃

 

Have fun checking the answer. I did.