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26 Apr 2019, 06:59
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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:
5%
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Question Stats:
91% (01:16) correct
9%
(01:48)
wrong
based on 1031
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The figure above represents an antenna tower with two guy wires that extend from point Q, 40 feet above the ground, to points P and R as shown. If the two wires have equal length, approximately what is the total length, in feet, of the two wires?
A. 60
B. 80
C. 100
D. 120
E. 180
PS06602.01
Quantitative Review 2020 NEW QUESTION
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2019-04-26_1758.png [ 9.87 KiB | Viewed 16527 times ]
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Archit3110
Major Poster
28 Apr 2019, 05:25
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∆ is right angled 3:4:5 factored by 10 so sides of each P & R = 50 each making bigger ∆ isoceles
sum = 100
IMO C
sum = 100
IMO C
Bunuel
23 May 2019, 06:30
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Solution
Given
In this question, we are given
- • The given figure represents an antenna tower with two guy wires that extend from point Q, 40 feet above the ground, to points P and R as shown.
• The two wires have equal length.
To Find
We need to determine
- • The total approximate length, in feet, of the two wires.
Approach & Working
As the lengths of two wires are same, PQ = QR.
Hence, PQR is an isosceles triangle.
- • In an isosceles triangle, a perpendicular from the top vertex to the base bisects the base.
• Therefore, each of the two right-angled triangles has a base of 30 feet.
Hence, we can say
- • \(QR^2 = 30^2 + 40^2 = 50^2\)
Or, QR = 50
Thus, the length of the two wires combined = (50 + 50) feet = 100 feet
Hence, the correct answer is option C.
