Answer:
(i) 2x²-19x+24 (ii) x = 1.5m
Step-by-step explanation:
(i) Width of the sidewalk is x (metre)
so dimensions of the swimming pool must be
l = 12 -2x
b = 7 - 2x
(we are subtracting 2x because sidewalk is on both sides)
given area of the pool is 36m²
So, (12-2x)(7-2x)=36
= 84-24x-14x+4x²=36
=> 4x²-38x+ 48 =0
=>2x²-19x+24
(ii) now solve the eq to get x
2x²-16x-3x+48=0
2x(x-8)-3(x-8)=0
(2x-3)(x-8)=0
Hence x = 3/2 = 1.5 (or) x = 8
When x = 1.5,
l = 9
b = 4
Area = lb = 9 x 4 = 36
When x = 8,
l = 12 - 2(8) = 12-16 = - 4
b = 7 - 2(8) = 7 - 16 = - 9
But distance cannot be negative, so x= 8 is not possible
Therefore x = 1.5m.
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Verified answer
Answer:
(i) 2x²-19x+24 (ii) x = 1.5m
Step-by-step explanation:
(i) Width of the sidewalk is x (metre)
so dimensions of the swimming pool must be
l = 12 -2x
b = 7 - 2x
(we are subtracting 2x because sidewalk is on both sides)
given area of the pool is 36m²
So, (12-2x)(7-2x)=36
= 84-24x-14x+4x²=36
=> 4x²-38x+ 48 =0
=>2x²-19x+24
(ii) now solve the eq to get x
2x²-16x-3x+48=0
2x(x-8)-3(x-8)=0
(2x-3)(x-8)=0
Hence x = 3/2 = 1.5 (or) x = 8
When x = 1.5,
l = 9
b = 4
Area = lb = 9 x 4 = 36
When x = 8,
l = 12 - 2(8) = 12-16 = - 4
b = 7 - 2(8) = 7 - 16 = - 9
But distance cannot be negative, so x= 8 is not possible
Therefore x = 1.5m.