A) \[\text{1806 }{{\text{m}}^{\text{2}}}\]
B) \[\text{1310 }{{\text{m}}^{\text{2}}}\]
C) \[\text{1360 }{{\text{m}}^{\text{2}}}\]
D) \[\text{1580 }{{\text{m}}^{\text{2}}}\]
E) \[\text{1284 }{{\text{m}}^{\text{2}}}\]
Correct Answer: C
Solution :
Let the breadth of the rectangular plot be x metres. Given width of the path \[\text{= 8m}\] Length of the path = length of the rectangular plot \[=(x+6)m.\] Now, (x) (x+6) - 8(x+6)=1040 \[\Rightarrow {{x}^{2}}+6x-8x-48=1040\] \[\Rightarrow {{x}^{2}}-2x-48-1040=0\] \[\therefore x=34m\] \[\therefore \]Length \[\text{=34+6=40m}\] \[\therefore \]Area of the rectangular plot \[\text{=40}\times \text{34=1360}{{\text{m}}^{\text{2}}}\]
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