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]