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Question

The area of a rectangle is given by the expression p(4p216). If the length of the rectangle is 4p(p2), then find the expression for the breadth of the rectangle.

A
2(p+2)
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B
p+2
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C
2(p2)
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D
p2
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Solution

The correct option is B p+2
Given, area of the rectangle = p(4p216) sq. units
Length of the rectangle = 4p(p2) units

Area of rectangle = length x breadth

p(4p216)=4p(p2)×breadth

breadth=p(4p216)4p(p2)

breadth=(4p216)4(p2)

breadth=(2p)2424(p2)

We know, a2b2=(a+b)(ab)

breadth=(2p4)(2p+4)4(p2)

breadth=2(p2)×2(p+2)4(p2)

breadth=4(p2)(p+2)4(p2)

breadth=(p+2) units

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