Question

Bosco wishes to start a 200 sq m rectangular vegetable garden. Since he has only 50m barbed wire,he fences three sides of the rectangular garden letting his house compound wall act as the fourth side of the fence.Find the dimensions of the garden.

Answer 1

l=40m or 10m
b=200/10=20m or b= 200/40=5m

Answer 2

Answer:

Dimensions of the garden are (20,10) Or (5,40)

Step-by-step explanation:

Dimensions of a rectangular vegetable garden:

Length = l m,

Breadth = b m,

Length of the barbed wire = 50m

According to the problem given,

l+b+l = 50 m

=> 2l+b = 50m

=> b = 50 - 2l ---(1)

$Area \: of \: the \: garden = 200\: m^{2}$

$\implies lb = 200\: m^{2}$

$\implies l(50-2l)=200\:[from(1)]$

$\implies 50l-2l^{2}=200$

/* Divide each term by 2, we get

$\implies 25l-l^{2}=100$

$\implies l^{2}-25l+100=0$

$\implies l^{2}-20l-5l+100=0$

$\implies l(l-20)-5(l-20)=0$

$\implies (l-20)(l-5)=0$

$\implies (l-20)=0\:Or\: (l-5)=0$

$\implies l=20\:Or\: l=5$

Case 1:

If l = 20, then b = 50-2l

=> b = 50 - 40 = 10,

Case 2:

If l = 5 ,then b = 50-2l

=> b = 50 - 10 = 40,

Therefore,

Dimensions of the garden are (20,10) Or (5,40)

•••♪