Kartik decided to make a swimming pool of dimensions 50 m X 40 m. A rectangular swimming pool has to be constructed that the area of the grass surrounding the pool would be 1184 m as shown in the figure. Find the length and breadth of the pool.
Answers
Length & breadth of pool = 34 & 24 m
Step-by-step explanation:
Total Area = 50 * 40 = 2000 m²
Area of Grass = 1184 m²
Area of Pool = 2000 - 1184 = 816 m²
Let say x m is left each side of pool
then dimension of pool = (50 - 2x) * (40 - 2x)
40 - 2x > 0 => x > 20
(50 - 2x) * (40 - 2x) = 816
=> 2000 - 100x - 80x + 4x² = 816
=> 4x² - 180x + 1184 = 0
=> x² - 45x + 296 = 0
=> x² -8x - 37x + 296 =0
=> x(x - 8) -37(x - 8) =0
=> (x - 37)(x - 8) = 0
x = 37 not possible as x > 20
x = 8
Dimension of pool = 50 - 2x & 40 - 2x
= 34 & 24 m
Length & breadth of pool = 34 & 24 m
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