The given information:
The ratio compounded of 4:5 and sub-duplicate of a:9 is 8:15.

Understanding the terms:
- Ratio: A comparison of two or more quantities.
- Compounded ratio: A compounded ratio is formed by multiplying or dividing the terms of two or more ratios.
- Sub-duplicate: Sub-duplicate of a number x is the number that satisfies the equation y^2 = x.
- a: A variable representing an unknown value.

Step 1: Understanding the compounded ratio
The compounded ratio is given as 4:5. This means that the ratio can be written as 4/5.

Step 2: Understanding the sub-duplicate ratio
The sub-duplicate ratio is given as a:9. This means that the ratio can be written as a/9.

Step 3: Combining the compounded and sub-duplicate ratios
The compounded ratio (4/5) and the sub-duplicate ratio (a/9) can be multiplied to form a new ratio. The resulting ratio is given as 8:15.

Step 4: Setting up the equation
To find the value of "a", we need to set up an equation using the given information. We can write the equation as follows:
(4/5) * (a/9) = 8/15

Step 5: Solving the equation
To solve the equation, we can cross multiply:
4 * a = 8 * (5/9) * 15

Simplifying the equation gives:
4a = 8 * 5 * 15 / 9

Step 6: Simplifying the equation
We can simplify the equation by canceling out common factors:
4a = (8/9) * (5/1) * (15/1)

Simplifying further gives:
4a = 40 * 15 / 9

Step 7: Finding the value of "a"
To find the value of "a", we can divide both sides of the equation by 4:
a = (40 * 15) / (9 * 4)

Simplifying the equation gives:
a = 600 / 36

Finally, simplifying further gives the value of "a":
a ≈ 16.67

A=2
4:5x√a:3=8:15
using propotion formula
4√a:15=8:15