The ratio of the length to the width of a rectangle is 8:3. What is the ratio of the width to the perimeter? Does this ratio depend on the actual width?

Question

• Solve the problems and show all of your thinking. You could use a double number-line model.

• Explain how you know each answer makes sense.

Answer 1

Let the length be 8x and width be 3x

p=2(l+w)=2(8x+3x)=2(11x)=22x

ratio of width to perimeter=3x:22x=3:22

This ratio does not depend on actual width.

For example

l=16cm  w=6cm   p=2(16+6)=44cm

l=24cm w=9cm   p=2(24+9)=66cm

The ratio of length to width  is 8:3 and ratio of width to perimeter is 3:22 in both the cases.