Question

a piece of wood is 180cm long, Tom cuts it into three pieces in the ratio 2:3:4
Work out the length of the longest piece

Answer 1

2:3:4
2:3:4 can be written as 2x:3x:4x

2x+3x+4x=180
9x=180
x=20 

Therefore it is
40:60:80

Answer 2

$The\ ratio\ is:2:3:4\\ Let's\ sum\ up\ it:\\ 2+3+4=9\\ \frac{2}{9}*180=40\\ \frac{3}{9}*180=60\\ \frac{4}{9}*180=80\\ The\ longest\ piece\ has\ lenth=80cm$