A rectangular enclosure is made from 40 m of fencing. The area enclosed is 96 m2. dimensions of the enclosure

A rectangular enclosure is made from 40 m of fencing. The area enclosed is 96 m2.
Find the dimensions of the enclosure.

(Perimeter)P=2(l+b)=40 ------ (i)
(Area)A=lb=96 ----------- (ii)
2(l+b)=40
l+b=20
l=20-b -------- (iii)
put (iii) in (ii),
(20-b)b=96
20b-b^2 = 96
b^2 - 20b + 96 = 0
b^2 - 12b - 8b + 96 = 0
b(b-12)-8(b-12)=0
(b-8)(b-12)=0
b-8=0; b-12=0
b=8; 8=12.

If b=8m, l=20-8=12m.
If b=12m, l=20-12=8m.

A rectangular enclosure is made from
40 m of fencing.
The area enclosed is 96 m2.
Find the dimensions of the enclosure.
L times B is 96 m^2
2L + 2B = 40 m
L + B = 20
LB = 96
L(20 - L) = 96
L^2 - 20L + 96 = 0
(L - 12)(L - 8) = 0
The dimensions of the enclosure:
Length = 12 m
Breadth = 8 m

Let x = length and y = width.
xy = 96
2x + 2y = 40
solve the system of equations:
x = 96/y
2(96/y) + 2y = 40
192/y + 2y = 40
192 + 2y^2 = 40y
96 + y^2 = 20y
y^2 - 20y + 96 = 0
(y - 12)(y - 8) = 0
y = 12 or y = 8
x = 96/12 = 8 or x = 96/8 = 12
length = 12m and width = 8m

let length = L and width = W

LW = 96

2(L+B)= 40
(L+B)=20


L=12, B=8