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

[AAPL]

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]

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
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[fskilnik@GMATH]

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]

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