In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?
144
216
324
360
396
OA is B Please explain
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- aneesh.kg
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Area of MPRS = Area of MPQT + Area of TQRS
540 = a*a + 12*a
(where 'a' is the side of the square MPQT or the breadth of rectangle MPRS)
a^2 + 12*a - 540 = 0
(a + 30)*(a - 18) = 0
a = 18 is the only positive root and hence the only possible value.
Area of TQRS = 18*12 = 216 sq. units
(B) is the answer
540 = a*a + 12*a
(where 'a' is the side of the square MPQT or the breadth of rectangle MPRS)
a^2 + 12*a - 540 = 0
(a + 30)*(a - 18) = 0
a = 18 is the only positive root and hence the only possible value.
Area of TQRS = 18*12 = 216 sq. units
(B) is the answer
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- aneesh.kg
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Well, that largely comes from practice. So, I'd suggest you to solve a lot of quadratic equations.
Anyway, for this problem, let me try to explain my thought-process.
a^2 + 12*a - 540 = 0
I knew that I had to split 12*a into two parts such that they multiply to -540*a^2. Since -540*a^2 is a negative number, one of the two parts should be positive and one should be negative. Then I went on looking for two numbers that multiply to 540 and whose difference is 12.
I tried out these pairs which multiply to 540:
20 and 17, doesn't work because the difference is 3.
30 and 18, Voila! It works! So, the two parts must be 30*a - 12*a.
It might look like a long procedure, but when you've practiced hundreds of quadratic expressions, it is a 5-second thing. So, Practice!
Anyway, for this problem, let me try to explain my thought-process.
a^2 + 12*a - 540 = 0
I knew that I had to split 12*a into two parts such that they multiply to -540*a^2. Since -540*a^2 is a negative number, one of the two parts should be positive and one should be negative. Then I went on looking for two numbers that multiply to 540 and whose difference is 12.
I tried out these pairs which multiply to 540:
20 and 17, doesn't work because the difference is 3.
30 and 18, Voila! It works! So, the two parts must be 30*a - 12*a.
It might look like a long procedure, but when you've practiced hundreds of quadratic expressions, it is a 5-second thing. So, Practice!
Aneesh Bangia
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
- aneesh.kg
- Master | Next Rank: 500 Posts
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Correction:
I meant 20 and 27
I meant 20 and 27
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- Scott@TargetTestPrep
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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:massi2884 wrote:In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?
144
216
324
360
396
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,
Answer: B
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