Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{540 \: m}}}}}[/tex]
Step-by-step explanation:
Let the length and breadth be 5x and 4x respectively.
Area of rectangular field = 18000 m²
Finding the value of x
Area of rectangle = [tex] \sf{l \times b}[/tex]
Plug the values
⇒[tex] \sf{18000 = 5x \times 4x}[/tex]
Calculate the product
⇒[tex] \sf{18000 = 20 {x}^{2} }[/tex]
Swap the sides of the equation
⇒[tex] \sf{20 {x}^{2} = 18000}[/tex]
Divide both sides of the equation by 20
⇒[tex] \sf{ \frac{20 {x}^{2} }{20} = \frac{18000}{20} }[/tex]
Calculate
⇒[tex] \sf{ {x}^{2} = 900}[/tex]
Squaring on both sides
⇒[tex] \sf{x = 30}[/tex]
Replacing the value of x in order to find the value of length and breadth
Length = [tex] \sf{5x = 5 \times 30 = 150 \: m}[/tex]
Breadth = [tex] \sf{4x = 4 \times 30 = 120 \: m}[/tex]
Finding the perimeter of the rectangular field
Perimeter of rectangle = [tex] \sf{2(l + b)}[/tex]
plug the values
⇒[tex] \sf{2(150 + 120)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{300 + 240}[/tex]
Add the numbers
⇒[tex] \sf{540 \: m}[/tex]
Hope I helped !
Best regards!!
