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Question

Taylor purchased a rectangular plot of area 634 m2. The length of the plot is 2 m more than thrice its breadth. The length and breadth respectively is _____ (approximate values).


A

34.6 m & 11.20 m

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B

88 m & 24 m

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C

32 m & 16 m

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D

44.6 m & 14.20 m

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Solution

The correct option is D

44.6 m & 14.20 m


Let, Length = x
Breadth = y

Given,
Area of Rectangle = 634 m2
Length : x
Thrice the breadth : 3y
2 more that thrice : 3y+2
So, x=3y+2

Area of the rectangle=length×breadth
634=xy634=(2+3y)y634=2y+3y23y2+2y634=0

This equation resembles the general form of quadratic equation ax2+bx+c=0.

Lets find the values of y satisfying the equation.(Roots of the equation)

y=b ±b2 4ac2a=2 ±22 4×3(634)2 × 3y=2 ±4 + 76086=2 ±76126y=2 ± 87.2466y=2+87.2466 or 287.2466y=14.20 or 14.87

Length is always positive.
y=14.20 m

x=2+3yx=2+3(14.20)=44.6 m

Length =44.6 m
Breadth =14.2 m


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