A rectangular pool 12 metres by 8 metres is surrounded by a walkway of with x meters. At what value of x will the area of the walkway equal the area of the pool?
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Answered by
1
Area of pool = l×b
= 12×8
= 96
Answered by
1
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.
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