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Re: In the figure shown above, line segment QR has length 12 and [#permalink]
how did you determine the height as 12, wouldn't the height be different from 12 as it is QR, and it is stated that only the MPQT is a square. So, we know that QR and TS can be 12, and with x that would make it 12+18, and that would be our base?
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Re: In the figure shown above, line segment QR has length 12 and [#permalink]
Expert Reply
The area of MPRS = the area of MPQT + the area of TQRS.

540 = x^2 + 12x --> x = 18.

The area of TQRS = 12*18 = 216.

Answer: B.
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Re: In the figure shown above, line segment QR has length 12 and [#permalink]
Expert Reply
x^2 + 12x - 540 = 0

We try to split 540 into two factors such that their difference is 12
540 = 54*10 = 18*3*10
You can see immediately that the 2 factors will be 18 and 30.

x^2 + 30x - 18x -540 = 0
(x + 30)(x - 18) = 0
x = 18
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Re: In the figure shown above, line segment QR has length 12 and [#permalink]
Expert Reply
Another approach

Area of rectangle.........Side QT.......Area of square.....Total area of the figure
(A) 144
(B) 216
(C) 324....................324/12=27.... 27*27 =729........... 729 + 324 = 1053
(D) 360
(E) 396

The total area was supposed to be 540 however it is 1053 hence we move up (go for smaller values). Now we know that answer is either A or B so we try any of them.


Area of rectangle.........Side QT.......Area of square.....Total area of the figure
(A) 144
(B) 216....................216/12 =18.....18*18 =324.......... 324 + 216 =540 (BINGO!)
(C) 324....................324/12=27.... 27*27 =729........... 729 + 324 = 1053
(D) 360
(E) 396

Answer is B.
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