a swimming pool 50m by 25 m is to be built with a walkway w meters wide around it write the total area of the pool and walk way in the form ax exponet 2 +bx+c
To find the total area of the pool and the walkway, let's break down the problem into smaller components.
1. Calculate the area of the pool: The pool measures 50m by 25m, so the area of the pool without the walkway is 50m * 25m = 1250 square meters (m²).
2. Calculate the dimensions of the pool including the walkway: Since the walkway surrounds the pool on all sides, the length and width of the pool will be increased by twice the width of the walkway. Therefore, the overall dimensions of the pool including the walkway will be (50m + 2w) by (25m + 2w).
3. Calculate the area of the expanded pool: To find the area of the expanded pool, we multiply its length by its width. So, the area of the expanded pool is (50m + 2w) * (25m + 2w).
4. Subtract the area of the original pool: To find the area of just the walkway, we subtract the area of the original pool from the area of the expanded pool. Therefore, the area of just the walkway is (50m + 2w) * (25m + 2w) - 1250m².
Now, we have the area of the walkway and the original pool. To express the total area in the form ax² + bx + c, we need to simplify the equation.
Let's expand the equation:
= (50m + 2w) * (25m + 2w) - 1250m²
= (50m * 25m) + (50m * 2w) + (25m * 2w) + (2w * 2w) - 1250m²
= (1250m²) + (100mw) + (50mw) + (4w²) - 1250m²
= 150mw + 4w²
Therefore, the total area of the pool and walkway is given by the expression 150mw + 4w², where "a" equals 150m, "b" equals 0 (since there is no term without the variable), and "c" equals 4w².