A square lawn is bounded on three sides by a path 4 m wide- If the area of the path is 7-8 that of the lawn- find the dimensions of the lawn-

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Standard X

Mathematics

Solving Using Quadratic Formula When D>0

A square lawn...

Question

A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is $\frac{7}{8}$ that of the lawn, find the dimensions of the lawn.

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Solution

Using s = the side length of the square lawn,
Area of just the lawn =
Area of path plus lawn =
Area of ONLY the path =

AND using the 7/8 information,

Solve for s, of course after first simplifying...
.
.

$s equals fraction numerator 96 plus square root of 96 squared plus 4 cross times 7 cross times 256 end root over denominator 14 end fraction$
$s equals fraction numerator 96 plus 2 to the power of 6 over denominator 14 end fraction$

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

Using s = the side length of the square lawn, Area of just the lawn = Area of path plus lawn = Area of ONLY the path = AND using the 7/8 information, Solve for s, of course after first simplifying... . .

A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is $\frac{7}{8}$ that of the lawn, find the dimensions of the lawn.