Can anyone help with this maths question?

a 5m(cubed) load of concrete is used to put a path around the outside of a square lawn at a botanical garden. The path is 10cm thick and 1m wide. Find the dimensions of the lawn.





Thank you so much

Can anyone help with this maths question?
Need to find the dimensions of the square.


Since path is 10cm = 0.1m thick and 1m wide then for each metre in length we use 0.1m^3 of concrete (1 x 1x 0.1)





5m^3/0.1 m^3 = 50 so that means the length around the lawn is 50m. i.e the perimeter of the lawn is 50m.





Since the lawn is square each side length is the same and is equal to 50/4= 12.5m.


Hence the lawn has side lengths of 12.5m.
Reply:I think the answer is 50m because all you have to do is times 5mx10mx1m=50m.......
Reply:Okay.





The path uses 5m^3 of concrete, which is equal to the length of the path times the width of the path times the thinkness of the concrete.





L x 1m x .1m = 5m^3





.1L =5 m^3





L= 50 m





This is the perimeter of the path. The path goes around a square, so the length of each side of the path is 50/4 or 12.5m.





But if you draw a picture of the lawn with the path around it, you will see that the overall perimeter of the path is greater than the perimeter of the lawn by 8 meters or 2 meters per side.





So, the dimensions of the lawn are 10.5 m by 10.5 m.
Reply:let x be the length of square lawn


then according to given condition


(2(2x + 2) + 2x )(0.1)(1) = 5


(4x + 4) (0.1) = 5


0.4x + 0.4 = 5


0.4x = 4.6


x = 11.5


so dimension of lawn is 11.5m x 11.5m





David your working is also ok but at the end


you need to reduce 1 meter from each side instead of 2 because it will replicate the reduction of sides.


So, the dimensions of the lawn are 11.5 m by 11.5 m.

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