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