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06 Jul 2018, 06:25
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B
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Difficulty:
95%
(hard)
Question Stats:
41% (03:03) correct
59%
(03:22)
wrong
based on 44
sessions
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In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS is inscribed in the triangle as shown in the figure. Find the side of the square?
Capture.PNG [ 4.97 KiB | Viewed 12970 times ]
A) \(3\)
B) \(\frac{120}{37}\)
C) \(4\)
D) \(\frac{40}{9}\)
E) \(\frac{120}{23}\)
Attachment:
Capture.PNG [ 4.97 KiB | Viewed 12970 times ]
A) \(3\)
B) \(\frac{120}{37}\)
C) \(4\)
D) \(\frac{40}{9}\)
E) \(\frac{120}{23}\)
06 Jul 2018, 07:02
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This question can be solved by using similarity of triangles, see the sketch attached.
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WhatsApp Image 2018-07-06 at 19.30.14.jpeg [ 67.04 KiB | Viewed 12950 times ]
07 Jul 2018, 01:48
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Princ
If we look at sides as of \(\triangle{ABC}\), 6, 8, 10, it tells us that it is 3:4:5 triangle..
Now let side of square be x and PQ is || to AC (opposite sides of square)
in \(\triangle{BPQ}\), the sides too will be in 3:4:5 = BQ : BP : x
so BP = \(\frac{4x}{5}\)
now \(\triangle{CPS}\) and \(\triangle{ABC}\) are also similar and hence 3:4:5 \(\triangle\)
now 3:4:5=PS:CS:CP=x:CS:CP
so 3 = x, so 5 = CP = \(\frac{5x}{3}\)
Now BP+CP=AB...........\(\frac{4x}{5}+\frac{5x}{3}=8.................\frac{12x+25x}{15}=8..............\frac{37x}{15}=8\).
\(x=\frac{8*15}{37}=\frac{120}{37}\)
B
Attachments
Capture.PNG [ 13.79 KiB | Viewed 12350 times ]
