MathRevolution wrote:

[

Math Revolution GMAT math practice question]

What is the perimeter of a rectangle?

1) The square of the diagonal is \(52\).

2) The area of the rectangle is \(24\).

\(? = {\text{perim}}\left( {{\text{rectangle}}} \right)\)

Excellent opportunity to GEOMETRICALLY BIFURCATE each statement alone:

\(\left( 1 \right)\,\,\,{\text{dia}}{{\text{g}}^{\,{\text{2}}}} = 52\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{diag}}\,\, > \,\,0} \,\,\,{\text{diag}}\,\,{\text{unique}}\,\,\,{\text{but}}\,\,\,{\text{INSUFF}}.\)

\(\left( 2 \right)\,\,\,{\text{area}} = 24\,\,\,\,\, \Rightarrow \,\,\,\,{\text{INSUFF}}{\text{.}}\)

(See the image attached!)

\(\left( {1 + 2} \right)\)

Let L and W be the length and width of our

focused-rectangle. Hence:

\(? = {\text{2}}\left( {L + W} \right)\)

\(\left( {1 + 2} \right)\,\,\left\{ \begin{gathered}

{L^2} + {W^2} = 52 \hfill \\

2LW = 2 \cdot 24\,\,\,\, \hfill \\

\end{gathered} \right.\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,{\left( {L + W} \right)^2} = 52 + 48 = 100\)

\({\left( {L + W} \right)^2} = 100\,\,\,\,\mathop \Rightarrow \limits^{L + W\,\, > \,\,0} \,\,\,\,L + W\,\,\,{\text{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 2\left( {L + W} \right)\,\,\,\,{\text{unique}}\)

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

Regards,

fskilnik.

Attachments

20Set18_5m.gif [ 22.84 KiB | Viewed 327 times ]

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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