Fraction of Perimeter

Question

If the side of a hexagon is increased from 20 cm to 24 cm, What fraction does the perimeter increase by?

So,is it one side of hexagon is increased or all sides of hexagon is increased by 4 cm.

I calculated by increasing all sides of the hexagon by 4 cm and brought the fraction as one sixth.

The choices given are

a. One sixth b. five fifth c.four tenths d. one fifth

Is it correct? or can someone explain me if its not correct, how to solve it?

Answer 1

Yes, every side is increased by 4cm. The answer isn't a sixth, though. The side was 20cm, and has grown by 4cm, so it has grown by 4/20 = 1/5. (Likewise, the perimeter was 120cm, and has grown by 24cm, so it has grown by 24/120 = 1/5.)

Answer 2

You have: $20*6=120$ cm as your perimeter

If you increase each side by 4 cm, you have $(20+4)*6=144$cm

Compare the ratio, $120:144$ becomes $1:\frac{6}{5}$.

Therefore, the perimeter of each side increased by $\frac{6}{5}-1=\frac{1}{5}$.