The length of a rectangular field is 2 m greater than three times its width. The area of the field is 1496 m2. What are the dimensions of the field?

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Answer 1 · 2018-03-09T12:04:44

Length and width of the field are $68 and 22$ meter respectively .

Let the width of the rectangular field is $x$ meter, then the

length of the field is $3x+2$ meter.

The area of the field is $A= x(3x+2)=1496$ sq.m

$:.3x^2+2x -1496=0$ Comparing with standard quadratic

equation $ax^2+bx+c=0; a=3 ,b=2 ,c=-1496$

Discriminant $D= b^2-4ac; or D =4+4*3*1496=17956$

Quadratic formula: $x= (-b+-sqrtD)/(2a)$ or

$x= (-2+-sqrt 17956)/6 = (-2+-134)/6$

$:. x= 132/6=22 or x= -136/6~~ -22.66$ . Width can not

be negative, so $x=22$ m and $3x+2=66+2=68$ m. Hence

length and width of the rectangular field is $68 and 22$ meter

respectively . [Ans]