Question

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The swimming pool at Spring Valley High School is a rectangle with a base of 65 meters and a height of 25 meters. Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Find an expression for the area of the tiled floor in square meters.

Answer 1

Draw a rectangle for the pool and label it as given. Draw another rectangle surrounding the pool rectangle.

Label the rectangle surrounding the pool as 2W +65 for the base and 2W+ 25 for the height.

The area of the larger rectangle, pool plus tile, is:
\[(2W+65)(2W+25)= area\]\[(2W+65)(2W+25)=4W ^{2}+180W+1625\]
Now subtract the area of the pool from the area of the pool plus tile.
\[4W ^{2}+180W+1625-1625=4W ^{2}+180W\]
So the expression for the area of the tile is:\[4W ^{2}+180W\]