Question

A $ 2.5 $ - kg bag of grass seed covers an area of $ 1200{\text{ }}{{\text{m}}^2}. $ How much seed is needed to cover a square park with side length $ 500\,{\text{m?}} $

Answer 1

Hint: Here we will use the area of the square and then the weight of the grass seed required to cover the area of the square. Here we will frame the equation and find the correlation between the given data and will find the required value.

Complete step by step solution:
Given that A $ 2.5 $ - kg bag of grass seed covers an area of $ 1200{\text{ }}{{\text{m}}^2}. $
Also, we have to cover the area of square with the side length of $ 500\;m $
Now, the area of the square can be given by the product of side with the side.
Area of square $ = $ side $ \times $ side
Place the values in the above equation –
Area of square $ = 500 \times 500 $
Simplify the above equation –
Area of square $ = 250000{m^2} $
Now, using the given data –
 $ 1200{m^2} $ requires $ 2.5 $ kg bag of grass seeds
 $ \therefore 250000\;{m^2} = ? $
Cross multiply and frame the equation –
 $ = \dfrac{{250000}}{{1200}} \times \dfrac{{2.5}}{1} $
Common factors from the numerator and the denominator cancel each other.
 $ = \dfrac{{2500}}{{12}} \times \dfrac{{2.5}}{1} $
Simplify the above expression –
 $ = 520.83 $ kg of grass seed
Hence, the square area will require $ 520.83 $ kg of grass seed.
So, the correct answer is “ $ 520.83 $ kg ”.

Note: Be careful in understanding the given word statements and frame the equations accordingly. Cross check and understand the given data and then start simplification. Always remember that Common factors from the numerator and the denominator cancel each other.
Always remember the difference between the area and perimeter. Area is the inside space or the region whereas the perimeter is the outer edge or the surface. Area is measured in square units whereas perimeter in units such as meter, centimetre. Do not forget to write the appropriate unit after the solution.