A) \[\text{972 }{{\text{m}}^{\text{2}}}\]
B) \[\text{640 }{{\text{m}}^{\text{2}}}\]
C) \[\text{840 }{{\text{m}}^{\text{2}}}\]
D) \[\text{954 }{{\text{m}}^{\text{2}}}\]
Correct Answer: A
Solution :
Let the breadth (b) be x m. \[\therefore \] Length \[(l)\text{ }=\left( \frac{3}{4}x \right)m\] Perimeter = 126 m \[\Rightarrow 2(l+b)=126\Rightarrow 2\left( \frac{3}{4}x+x \right)=126\] \[\Rightarrow \frac{7x}{4}=63\Rightarrow x=\frac{63\times 4}{7}=36\] So, breadth = 36 m and length \[=\frac{3}{4}\times 36=27m\] \[\therefore \text{Area = (36 }\!\!\times\!\!\text{ 27) }{{\text{m}}^{\text{2}}}\text{ = 972 }{{\text{m}}^{\text{2}}}\]
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