# 9.2.1. Ratio

Determine the four proportional numbers of which the fourth proportional equals the square of the second, the first is less than the second by 1, and the third is 72.

• A or
• B or
• C or
• D or

### Example

Determine the four proportional numbers of which the fourth proportional equals the square of the second, the first is less than the second by 1, and the third is 72.

### Solution

Use , , , and to express and in terms of . Substitute into the ratio to find the values.

So:

• The first, , is less than the second, , by 1
• The fourth proportional, , equals the square of the second,

Note: The third proportional .

Now, , , , and are proportional

Substitute , , and

Since there are two possible values for , there are two sets that satisfy the conditions.

Use to find the first set of proportional numbers.

Substitute into and

Therefore, the first set is , , 72, and 64.

Use to find the second set of proportional numbers.

Substitute into and

Therefore, the second set is 8, 9, 72, and 81.

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