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17 Aug 2017, 23:34
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
97% (01:05) correct
3%
(02:10)
wrong
based on 53
sessions
History
Date
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Not Attempted Yet
In the figure above, MNO and OPM are isosceles right triangles. What is the length of OP?
(A) 8
(B) 10
(C) 5√3
(D) 7√2
(E) 5√5
Attachment:
2017-08-18_1026.png [ 11.24 KiB | Viewed 4457 times ]
18 Aug 2017, 00:22
Kudos
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MNO is an isosceles right triangle.
It implies OM= Square root of (25+25) = 5 *(square root 2)
Now again OMP is isosceles right triangle. So
OP= Square root of (50+50)=10
Sent from my MotoG3 using GMAT Club Forum mobile app
It implies OM= Square root of (25+25) = 5 *(square root 2)
Now again OMP is isosceles right triangle. So
OP= Square root of (50+50)=10
Sent from my MotoG3 using GMAT Club Forum mobile app
18 Aug 2017, 10:25
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Bunuel
Both isosceles right triangles have legs of equal length. Hence both legs of small triangle have length 5. Find the length of the hypotenuse MO of the small triangle, which is the leg of the larger triangle. Then use that length to find OP, hypotenuse of large triangle.
1. Length of MO, where legs NO = MN = 5
Find length of hypotenuse MO with Pythagorean theorem,** or use property of isosceles right triangles (45-45-90), whose sides have ratio
\(1: 1: \sqrt{2}\)
Legs NO and MN = 5, so MO=\(5\sqrt{2}\)
2. Find OP
MO is one of the legs of large triangle OPM.
MO = \(5\sqrt{2}\)
By side ratio property, hypotenuse OP = \(5\sqrt{2} * \sqrt{2}\)
\(5 * 2 = 10\)
Answer B
**
For MO (=x): \(5^2 + 5^2 = x^2\)
50 = \(x^2\)
x = \(5\sqrt{2}\)
For OP (=x):
Legs have equal length. MO =\(5\sqrt{2}\) = MP
\((5\sqrt{2})^2 +\\
(5\sqrt{2})^2 = x^2\)
100 = \(x^2\)
x = 10 = OP
