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Question

# Area of a rectangle whose length is greater than breadth is given by 25a2âˆ’35a+12. Match the following when a=4.

A
272 sq units
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B
16 units
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C
66 units
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D
17 units
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Solution

## Here, area is given in terms of a quadratic expression in one varaible. To find the possible length and breadth of a rectangle, we have to factorise the given expression. Area=25a2−35a+12 (Area=l× b)=25a2−20a−15a+12(splitting middle term)=5a(5a−4)−3(5a−4)=(5a−4)(5a−3) Since Length is greater than breadth, 5a−3 is the length and 5a−4 is the breadth. When a=4, Length =5a−3=5(4)−3=17 Breadth =5a−4=5(4)−4=16 Perimeter =2((5a−3)+(5a−4))=2(17+16)=66 units Area =(5a−3)(5a−4)=17×16=272 sq units.

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