A square pool is being built with an additional square decking area around it. The area of the decking alone is 64 square meters, and the total area (pool plus decking) is 144 square meters. What are the dimensions of the pool

Let the side length of the pool be \( x \) meters.

### Step 1: Write an expression for the total area.
The total area (pool plus decking) is 144 square meters. So, the side length of the entire structure (pool + decking) is \( x + 2d \), where \( d \) is the width of the decking on each side of the pool. The total area is therefore:
\[
(x + 2d)^2 = 144
\]

### Step 2: Write an expression for the decking area.
The decking area alone is given as 64 square meters. The area of the pool is \( x^2 \), so the decking area is the difference between the total area and the pool's area:
\[
(x + 2d)^2 - x^2 = 64
\]

### Step 3: Solve for the dimensions of the pool.
Using the total area equation:
\[
x^2 + 4xd + 4d^2 = 144
\]
Substitute \( d = \frac{x}{2} - x} \`` Would you like: 


 
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A square pool is being built with an additional square decking area around it. The area of the decking alone is 64 square meters, and the total area (pool plus decking) is 144 square meters. What are the dimensions of the pool?

Find the dimensions of a square pool with an additional decking area. The total area is 144 square meters, and the decking area alone is 64 square meters. This problem involves algebraic and geometric concepts and is suitable for students in Grades 9-10.

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