A rectangular pool 6 meters by 4 meters is surrounded by a walkway of width x meters. At what value of x will the area of the walkway equal the area of the pool .
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Answers
Required Answèr :-
- x = 1 m
*Step-by-step explanation:
Area of pool = 6×4= 24 m²
Area of walkway = (6+2x)(4 +2x) - 24
=24 + 12x + 8x + 4x² - 24
=4x² + 20x
★If the areas are equal, then,
4x² + 20x = 24
x² + 5x - 6 = 0
x = (-5 ±√25+24)/2
x = (-5 ± 7)/2
x = 1 and
x = -6 (excluded as negative)
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The value of x is 2 metres for the area of the walkway to be equal to the area of the pool.
Given the pool dimensions are 12 metres and 8 metres.
Area of the pool is length × breadth .
Area (pool) = 12×8 = 96 sq. m (Equation 1)
Now the walkway is x metres wide surrounded to the pool on all sides,
Dimensions of the complete pool (with walkway) is -
Length = (12+2x) m
Breadth = (8+2x) m
Now complete arera of the pool (with walkway) = (12+2x) × (8+2x)
Area (pool + walkway) = 96 + 40x + 4x² (Equation 2)
Now area of the walkway = area(pool + walkway) - area(pool)
area(walkway) = 40x + 4x² + 96 - 96 = 4x² + 40x
Now we have to find a value so that the area of the pool is equal to the area of the walkway.
Area(walkway) = Area(pool)
4x² + 40x = 96
4x² + 40x - 96 = 0
x² + 10x - 24 = 0
x² + 12x - 2x - 24 = 0
x(x+12) - 2(x+12) = 0
(x+12)(x-2) = 0
Therefore, x=2 or x=-12
Length cannot be negative, therefore x=2 is the solution of the equation
When the walkway is 2 m wide the area of the pool and the area of the walkway is same.