The rectangular pool is surrounded by a 1 m wide walkway. One side of the pool is 15 m smaller than the other.

The rectangular pool is surrounded by a 1 m wide walkway. One side of the pool is 15 m smaller than the other. The pool area is 74 m2. less area occupied by the pool together with the path. Find the dimensions of the pool.

1. Let’s denote the width of the pool by X, and its length by Y.

2. Then the first equation of the problem: X + 15 = Y.

3. Pool area without track S1 = X * Y.

4. The walkway increases both the width and the length of the pool by 2 meters. Pool area, taking into account the track S2 = (X + 2) * (Y + 2).

5. The third equation of the problem: S1 + 74 = S2. Or X * Y + 74 = (X + 2) * (Y + 2).

6. Open the brackets in the second equation and substitute the expression for Y from the first equation. We get: X ^ 2 + 15 * X + 74 = X ^ 2 + 17 * X + 2 * X + 34,

7. Here are similar terms. We get: 4 * X = 40. That is, X = 10.

8. From the first equation Y = 25.

Answer: the dimensions of the pool are: width – 10 m, length – 25 m.