divide 24 in two parts such that they are in AP and their product is 440

Please check, the question should be to divide 24 into three parts. The solution is as follows:

 

The parts are in AP, so let the parts be a-d, a and a+d

where the first term =a-d

the common difference =d

Given, sum =24cm

a-d + a+a + d = 24cm

3a = 24cm

a =8cm

Given: Product of the terms = 440

(a-d) (a) (a+d) = 440

(8-d) (8+d) (8) =440

(8-d)(8+d) = 55

8² -d² = 55

64 - d² = 55

d² = 64-55

d² = 9

d = +3, -3

When d = 3,

AP- a-d , a, a+d

so the AP is 8-3, 8, 8+3

AP = 5, 8, 11

When d = -3, AP = 11, 8, 5

 

So, the three parts are 5, 8, 11.