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Question

Area of a rectangle whose length is greater than breadth is given by 25a235a+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=25a235a+12 (Area=l× b)=25a220a15a+12(splitting middle term)=5a(5a4)3(5a4)=(5a4)(5a3)

Since Length is greater than breadth, 5a3 is the length and 5a4 is the breadth.

When a=4,
Length =5a3=5(4)3=17
Breadth =5a4=5(4)4=16
Perimeter =2((5a3)+(5a4))=2(17+16)=66 units
Area =(5a3)(5a4)=17×16=272 sq units.

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