Question

the area of a rectangular field is 18000m^2 if the ratio of length and breath is 5:4 find its perimeter

Answer 1

`\boxed{ \bold{ \huge{ \boxed{ \sf{540 \: m}}}}}`

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 =
`\sf{l * b}`

Plug the values

⇒
`\sf{18000 = 5x * 4x}`

Calculate the product

⇒
`\sf{18000 = 20 {x}^(2) }`

Swap the sides of the equation

⇒
`\sf{20 {x}^(2) = 18000}`

Divide both sides of the equation by 20

⇒
`\sf{ \frac{20 {x}^(2) }{20} = (18000)/(20) }`

Calculate

⇒
`\sf{ {x}^(2) = 900}`

Squaring on both sides

⇒
`\sf{x = 30}`

Replacing the value of x in order to find the value of length and breadth

Length =
`\sf{5x = 5 * 30 = 150 \: m}`

Breadth =
`\sf{4x = 4 * 30 = 120 \: m}`

Finding the perimeter of the rectangular field

Perimeter of rectangle =
`\sf{2(l + b)}`

plug the values

⇒
`\sf{2(150 + 120)}`

Distribute 2 through the parentheses

⇒
`\sf{300 + 240}`

Add the numbers

⇒
`\sf{540 \: m}`

Hope I helped !

Best regards!!