Question

If a:9= 18:a, Calculate the positive value of a

Answer 1

Hi,

`a=9√(2)`

Explanation:

The statement "a:9 = 18:a" represents a proportion.

To find the positive value of "a," you can cross-multiply and then solve for "a." Here's how you can do it:

a:9 = 18:a

`(a)/(9)=(18)/(a) \\`

Cross-multiplying:

a * a = 9 * 18

`a^2=2*9^2\\\\a^2-2*9^2=0\\\\(a-9√(2) )(a+9√(2) )=0\\a=9√(2) \ or\ a=-9√(2)`

Now, to find the positive value of "a,"

`a = 9√(2)\\\\a \approx{ 12.73}\\`

So, the positive value of "a" is approximately 12.73.