URGGEEENNNTTT!!!! GRADE 11 MATHHH!!!! 50 POINTS!!!?

Question

A rectangular pool measuring 10m by 4m is surrounded by a deck of uniform width. The combined area of the deck is 135m^2. What is the width of the deck?

Answer 1

Let x be width of the desk.

Length and breadth of the rectangular pool be 10m and 4m.

If the desk surrounds  the pool, it adds 2x to the dimension of the pool.

The area of both pool and desk is 135m².

(2x + 10)(2x +4) = 135

4x² + 8x + 20x + 40 = 135

4x² + 28x + 40 = 135

4x² + 28x + 40 - 135 = 0

4x² + 28x - 95 = 0

4x² + 38x - 10x - 95 = 0

2x(2x + 19) - 5(2x + 19) = 0

(2x - 5 ) (2x + 19) = 0

2x - 5 = 0 or 2x + 19 = 0

2x = 5 or 2x = -19

x = 5/2 or x = -19/2

Since there can't be negative distances, take only the positive solution.

x = 5/2 = 2.5m

Therefore the width of the desk is 2.5 meters.