Find the area

Question

A small city park consists of a rectangular lawn surrounded on all sides by a 330 cm² border of flowers 2.5m wide. Find the area of the lawn if the entire park is 5m longer than it is wide. 

Answer 1

Sean,

If your measurements are correct, the area of the lawn is ZERO!

If we let the width be zero and the length is 0+5m, then along one length of 5m, the area of a border is 2.5m times 5m = 12.5m² which converts to 125,000cm² . That already greatly exceeds the given area of 330cm²!

Can you double check your problem to see if something needs to be changed?

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I just found a similar problem which gave the border area as 330m².

Here is its solution.

 

Let x = width of the lawn and x+5=length of the lawn.
The border consists of two strips of area (2.5*x) =2.5x m² ; two strips of area 2.5*(x+5) = (2.5x + 12.5) m² and four corner squares each with area 2.5*2.5 = 6.25 m².
So the total area of the border is
2*(2.5x) + 2*[2.5*(x+5)] +4*6.25 = 10x + 50 = 330
Solving for x gives x = 28m and length = (28+5)m = 33m, so area of lawn is 28m*33m = 924m².