NoHalfMeasures wrote:

The figure above represents a rectangular garden bordered by a walkaway that has a uniform width of 3 feet. What's the perimeter of the garden?

(1) The outer perimeter of the walkway is 124 feet

(2) The area of the garden is 600 feet

squared.

All lengths are considered in feet.

\(? = 2\left[ {\left( {a - 6} \right) + \left( {b - 6} \right)} \right]\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,\,? = a + b\,\,}\)

\(\left( 1 \right)\,\,\,2\left( {a + b} \right) = 124\,\,\,\, \Rightarrow \,\,\,\,? = a + b\,\,\,{\text{unique}}\)

\(\left( 2 \right)\,\,\left( {a - 6} \right)\left( {b - 6} \right) = 600\,\,\,\,\left\{ \begin{gathered}

\,{\text{Take}}\,\,\left( {a,b} \right) = \left( {16,66} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{16 + 66}}\,\, \hfill \\

\,{\text{Take}}\,\,\left( {a,b} \right) = \left( {26,36} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{26 + 36}} \ne {\text{16 + 66}}\,\, \hfill \\

\end{gathered} \right.\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)

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