In the figure shown above, line segment QR has length 12,

Question

Official Guide In the figure shown above, line segment has length of 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS? A. 144 B. 216 C. 324 D. 360 E. 396 OA B.

Jay@ManhattanReview · Answer

AAPL wrote:Official Guide In the figure shown above, line segment has length of 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS? A. 144 B. 216 C. 324 D. 360 E. 396 OA B. The question is posted correctly. The correct version is this: In the figure shown above, line segment QR has length of 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS? Area of MPRS = Area of MPQT + Area of TQRS Say the length of the square MPQT = x, thus, Area of MPQT = x^2 And, Area of TQRS = 12.x So, 540 = x^2 + 12x => x = 18. Area of TQRS = 12*18 = 216 The correct answer: B Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review Dilsukhnagar | GMAT Prep Begumpet | GRE Prep Visakhapatnam | Warangal GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

fskilnik@GMATH · Answer

AAPL wrote:Official Guide In the figure shown above, line segment QR has length of 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS? A. 144 B. 216 C. 324 D. 360 E. 396 $$? = S$$ $$540 = \frac{S}{{12}}\left( {12 + \frac{S}{{12}}} \right)\,\,\mathop = \limits^{x\,\,\left( {aux} \right)\,\, = \,\,\,S/12} \,\,\,x\left( {12 + x} \right)$$ $$540 = 54 \cdot 10 = 27 \cdot 2 \cdot 10 = {3^3} \cdot {2^2} \cdot 5\,\,\,\,\mathop \Rightarrow \limits^{12\,\,{\text{difference}}} \left\{ \begin{gathered} \boxed{x = {3^2} \cdot 2 = 18} \hfill \ 12 + x = 3 \cdot 2 \cdot 5 = 30 \hfill \ \end{gathered} \right.$$ $$\frac{S}{{12}} = x = 18\,\,\, \Rightarrow \,\,? = S = 12 \cdot 18 = 180 + 36 = 216$$ This solution follows the notations and rationale taught in the GMATH method.

Scott@TargetTestPrep · Answer

AAPL wrote:Official Guide In the figure shown above, line segment has length of 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS? A. 144 B. 216 C. 324 D. 360 E. 396 Since PQMT is a square, we can let PQ = PM = n. Since QR = 12, PR = n + 12. Finally, since the area of rectangle MPRS is 540, we have: n(n + 12) = 540 n^2 + 12n = 540 n^2 + 12n - 540 = 0 (n + 30)(n - 18) = 0 n = -30 or n = 18 Since n can’t be negative, n = 18, and the area of square MPQT is 18 x 18 = 324. Thus, the area of rectangle TQRS is 540 - 324 = 216. (Or the area of rectangle TQRS is 18 x 12 = 216.) Answer: B

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