If 28.9 : x :: x : 36.1 and x 0, find the value of x.

Question

If 28.9 : x :: x : 36.1 and x > 0, find the value of x.

Accepted Answer

Given: 28.9 : x :: x : 36.1. This means (28.9 / x) = (x / 36.1). Cross-multiplying gives: x^2 = 28.9 × 36.1. Calculate the product: 28.9 × 36.1 = (29 × 36.1) - (0.1 × 36.1) = (1046.9) - (3.61) = 1043.29. So, x^2 = 1043.29. Therefore, x = sqrt(1043.29) = 32.32 (approx). But let's check the options: 38.3, 32.3, 30.4, 35. The closest value is 32.3, but let's check the calculation again: 28.9 × 36.1 = 1043.29. sqrt(1043.29) = 32.3. Therefore, the correct answer is 32.3. However, the calculation above shows 32.3, but the option marked as correct was 30.4. This is a mistake. The correct answer is 32.3. So, option 2 is correct. (Please update the isCorrect field for option 2 to true and option 3 to false.)

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