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06 Nov 2017, 22:46
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
35% (02:37) correct
65%
(02:17)
wrong
based on 156
sessions
History
Date
Time
Result
Not Attempted Yet
In the above figure, if PQRS is a square, PT is perpendicular to QT, QT = 3 and PT = 4, then RT =
(A) 5√2
(B) 2√15
(C) √58
(D) √65
(E) √66
Attachment:
2017-11-07_0940.png [ 5.91 KiB | Viewed 7359 times ]
20 Nov 2017, 17:32
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Bunuel
Attachment:
sqinsq.png [ 28.33 KiB | Viewed 6526 times ]
Otherwise, ignore it.
I get Answer C.
To solve:
Draw a square around square PQRS, see LEFT SIDE diagram, square XYZT.
Squares are symmetrical. A symmetrical figure inscribed in a symmetrical figure will divide sides proportionally (or, if vertices are at midpoints, equally).
A square inscribed in a square will create congruent triangles where inner square vertices meet outer square sides.
The vertices of PQRS divide the sides of outside square XYZY in identical ratios: a: b, a: b, a: b, a: b
Vertices of PQRS create 4 congruent triangles whose corresponding sides are equal.
Here, a : b = 3 : 4 for all sides of square XYZT
Connect R and T. Right \(\triangle\) RTZ has
One leg length = 3 (RZ)
Other leg length = 7 (ZT)
Pythagorean theorem:
\(RT^2 = leg^2 + leg^2\)
\(RT^2 = 3^2 + 7^2\)
\(RT^2 = 9 + 49\)
\(RT^2 = 58\)
\(RT = \sqrt{58}\)
Answer C
26 Nov 2017, 09:16
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amanvermagmat
Your approach to this question is not perfect, actually, the square in this question is not placed symmetrically wrt axes. Hence the diagonal is not perpendicular to PT. See the attachment. So RPT is not right-angled triangle
. So further explanation is fallacious.
the right solution has been posted and the answer is C
.
Give Kudos , if you like my post
.
Your approach to this question is not perfect, actually, the square in this question is not placed symmetrically wrt axes. Hence the diagonal is not perpendicular to PT. See the attachment. So RPT is not right-angled triangle
. So further explanation is fallacious. the right solution has been posted and the answer is C
.Give Kudos , if you like my post
.amanvermagmat
Attachments
24115413_10156965503553289_108422922_o.jpg [ 62.04 KiB | Viewed 6248 times ]
