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Sagot :
At x = 2 ,The area of the walkway equals the area of pool.
To find the area of the walkway, we have to subtract the total area (pool plus walkway) with the pool area.
Thus, first we calculate these two:
Pool area:
[tex]A_{Pool Area} = Breadth * Height[/tex]
Total area (pool plus walkway):
[tex]A_{total area}[/tex] = (x +12 +x) (x + 8 + x)
= (12 +2x) (8 +2x)
= 96 + 24x +16x +4x²
= 4x² + 40x + 96
Therefore, the Walkway area:
The walkway area can found by subtracting the pool are from the total area:
[tex]A_{Total area} - A_{pool Area} = A_{walkway}[/tex]
[tex]A_{walkway}[/tex] = 4x² + 40x + 96 -96
= 4x² + 40x
Now, the problem is asking for x value that makes equal the pool area and the walkway area.
[tex]A_{walkway}[/tex] = 4x² + 40x = 96
⇒ 4x² +40x - 96 = 0
⇒ 4( x² + 10x - 24) =0
⇒ x² + 10x - 24 = 0
Now,
we factorize this quadratic expression:
x² + 10x - 24 = 0
⇒ (x + 12) (x - 2) = 0
Therefore,
x = -12
and
x = 2
The correct answer is 2, we put the value 2 in the walkway equation, we get:
x² + 40x
]= (2)² + 40× 2
= 4 + 80
= 84 m²
(We ignore the negative 12)
Learn more about Area:
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