The lengths of the sides of a triangle are in the extended ratio 7 : 8 : 9. The perimeter of the triangle is 72 cm. What are the lengths of the sides?

a=21, b=24, c=27

Step-by-step explanation:

a = side 1, b = side 2, c = side 3

a+b+c=72

a/b=7/8 and b/c=8/9 (proportion it)

then cross multiply to get 8a=7b and 9b=8c---> divide to get a=7/8b and c=9/8b

put that into the first equation--> 7/8b+8/8b+9/8b=72

add the fractions to get 24/8b=72 (24/8 equals 3) so 3b=72 (divide to get b=24)

then fill that in to the above equations (8a=7b, 9b=8c)

8a=7 (24) and 9 (24) = 8c---> 8a=168 and 8c=216

divide all that and get a=21 and c=27

with all the measurements, you can check the proportion to make sure it works (7:8:9-->21:24:27)

if you multiple 7, 8, and 9 by 3 then you get the numbers found so it works