Question

If three numbers are in the ratio of 1:2:3 and half the sum is 18, then the ratio of squares of the numbers is:

(a) 6:12:13
(b) 1: 2:4
(c) 36:144: 324
(d) None of these​

Answer 1

The ratio of the squares of the given numbers is 36:144:324.

Step-by-step explanation:

The given ratios are 1:2:3. Let's assume the numbers represented by these ratios are x, 2x, and 3x.

Half the sum of these numbers is 18, so (x + 2x + 3x)/2 = 18.

By solving this equation, we get 6x/2 = 18.

Simplifying further, we have 3x = 18.

Dividing both sides by 3, we find that x = 6.

Therefore, the numbers are 6, 12, and 18.

The ratio of the squares of these numbers is (6^2):(12^2):(18^2), which simplifies to 36:144:324.

So, the correct answer is option (c) 36:144:324.