Question

Divide 216 into three parts which are in A.P. and the product of two smaller parts is 5040.

Answer 1

Let the three parts of 216 in A.P. be (a – d), a, (a + d).

`\implies` a – d + a + a + d = 216

`\implies` 3a = 216

`\implies` a = 72

Given that the product of two smaller parts is 5040.

`\implies` a(a – d) = 5040

`\implies` 72(72 – d) = 5040

`\implies` 72 – d = 70

`\implies` d = 2

∴ a – d = 72 – 2 = 70, a = 72 and a + d = 72 + 2 = 74

Therefore, the three parts of 216 are 70, 72 and 74.