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2 years ago

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

Mathematics

1 answer:

zavuch27 [327]2 years ago

8 0

Answer:

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

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 = $\sf{l \times b}$

Plug the values

⇒ $\sf{18000 = 5x \times 4x}$

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

⇒ $\sf{ \frac{20 {x}^{2} }{20} = \frac{18000}{20} }$

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 = $\sf{5x = 5 \times 30 = 150 \: m}$

Breadth = $\sf{4x = 4 \times 30 = 120 \: m}$

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!!

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