The length of a rectangular field is 12m more than width.The value of its area= 4 times the value of its perimeter. Find dimensions of the field.

We have to find the length of a rectangular given that the
length is 12m more than the width and the numeric value of the area is four times that
of the perimeter.

Let the length be L adn the width be
W

The perimeter is 2*(L +
W)

The area is L*W

The length
is 12m more than the width, L = W + 12

Area  = W*(W + 12) =
4* 2*(W + 12 + W)

=> W^2 + 12W = 8*(2W +
12)

=> W^2 + 12W = 16W +
96

=> W^2 - 4W - 96 =
0

=> W^2 - 12W + 8W - 96 =
0

=> W(W - 12) + 8(W - 12) =
0

=> W = 12 or -8

The
width cannot be negative, so we take width = 12

The length
= 12 + 12 = 24

The dimensions of the
rectangle are 12m W by 24m L.