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Question

A square lawn is bounded on three sides by a path of 4m wide. If the area of the path is 78 that of the lawn, find the dimensions of the lawn.


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Solution

Step 1. Finding the area of square lawn and path:

Let the length of the side of the square lawn be xm.

The area of square lawn =side×side=x2m2
The area of the path =(x+8)×4+x×4+x×4

=8x+4x+32

=12x+32m2
Step 2. Finding the dimensions of the lawn:

Now, the area of the path is 78 that of the lawn.

12x+32=78x296x+256=7x27x2-96x-256=07x2-112x+16x-256=07x(x-16)+16(x-16)=0(7x+16)(x-16)=0x=16m,-167m

But the length cannot be negative.
Thus, the dimensions of the square lawn is 16m.


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