Question

A farmer wishes to enclose a rectangular plot with a wire fence. The width of the plot is 3 metres less than its length (x). The area enclosed by the fence is 378 square metres. Form an equation in x and hence find the length of the plot.

Help​

Answer 1

• Length is x
• Width be x-3

`\\ \rm\rightarrowtail Area=Length* Width`

`\\ \rm\rightarrowtail x(x-3)=378`

`\\ \rm\rightarrowtail x^2-3x=378`

`\\ \rm\rightarrowtail x^2-3x-378=0`

`\\ \rm\rightarrowtail x^2-21x+18x-378=0`

`\\ \rm\rightarrowtail (x+18)(x-21)=0`

`\\ \rm\rightarrowtail x=-18,21`

Take it positive

• Length=21m

Answer 2

Let the length be x

Let the width be x-3

Now,

`\red \dashrightarrow \mathcal{Area = Length×Breadth}`

• Area is given i.e. 378 m²

`\red \dashrightarrow \sf \: 378 = x * (x - 3)`

`\red \dashrightarrow \sf \: 378 = {x}^(2) - 3x`

`\red \dashrightarrow \sf \: 378 - {x}^(2) + 3x = 0`

`\red \dashrightarrow \sf \: - 378 + {x}^(2) - 3x = 0`

`\red \dashrightarrow \sf \: {x}^(2) - 3x - 378= 0`

`\red \dashrightarrow \sf \: {x}^(2) + 18x - 21x - 378= 0`

`\red \dashrightarrow \sf \: x * (x + 18) - 21(x + 18)= 0`

`\red \dashrightarrow \sf \: (x + 18) (x - 21)= 0`

`\red \dashrightarrow \sf \: x + 18= 0 \\ \red \dashrightarrow \sf \: x - 21= 0`

`\red \dashrightarrow \sf \: x = - 18 \\ \red \dashrightarrow \sf \: x = 21`

• Since the dimension cannot be in negative, We will consider x is 21

`\colorbox{lightyellow}{length = x = 21}`

`\colorbox{lightyellow}{breadth= x - 3= 21 - 3 = 18}`