The swimming pool at Spring Valley High School is a rectangle with a width of 65 meters and a length of 30 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.
Answers
Answer:4w^2 + 190w
Step-by-step explanation:
(2w + 30)(2w + 65)
= 4w2 + 130w + 60w + 1950
= 4w2 + 190w + 1950
(4w2 + 190w + 1950) − 1950
The area of the tiled floor is 4w² + 190w
Given:
The swimming pool at Spring Valley High School is a rectangle with a width of 65 meters and a length of 30 meters.
Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides.
To find:
Find an expression for the area of the tiled floor
Solution:
Formula used:
Area of rectangle = Length × Width
From the data, Length = 30 meters and width = 65 meters
Area of the swimming pool = [ 65 × 30 ] = 1950 m²
Given that the four sides are extended by 'w' meters
Length of the pool after extension = 30 + 2w
Width of the pool after extension = 65 + 2w
Area of the pool with extension = (30 + 2w) × (65 + 2w)
= 1950 + 60w + 130w + 4w²
= 4w² + 190w + 1950
Area of the tiled floor = Area of pool with extension - Area of pool initially
= 4w² + 190w + 1950 - 1950 = 4w² + 190w
Therefore,
The area of the tiled floor is 4w² + 190w
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