Question

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?

Answer 1

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

Explanation:

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]