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The figure above represents a semicircular archway over a flat street.
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22 Jun 2018, 00:30
22 Jun 2018, 00:30
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The figure above represents a semicircular archway over a flat street. The semicircle has a center at O and a radius of 6 feet. What is the height h, in feet, of the archway 2 feet from its center?
A. √2
B. 2
C. 3
D. 4√2
E. 6
(PS05957)
Attachment:
PS05957_f009.jpg [ 34.62 KiB | Viewed 41920 times ]
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Re: The figure above represents a semicircular archway over a flat street.
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22 Jun 2018, 05:24
22 Jun 2018, 05:24
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Solution
Given:
- • The figure depicts a semi-circular archway over a flat street
• The semi-circle has a center at O and a radius of 6 feet
To find:
- • The length of the height h, in feet, of the archway 2 feet from its center
Approach and Working:
If we add the point O and A, we get a right-angled triangle OAB, right-angled at point B and hypotenuse AO
As the radius is 6 feet, we can say
- • AO = 6 feet
Applying Pythagoras Theorem in triangle OAB, we can write:
- • \(AO^2 = AB^2 + BO^2\)
Or, \(6^2 = h^2 + 2^2\)
Or, \(h^2 = 36 – 4 = 32\)
Or, \(h = 4\sqrt{2}\)
Hence, the correct answer is option D.
Answer: D
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Joined: 12 Sep 2015
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Re: The figure above represents a semicircular archway over a flat street.
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Updated on: 15 Mar 2020, 05:36
Updated on: 15 Mar 2020, 05:36
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Bunuel
The figure above represents a semicircular archway over a flat street. The semicircle has a center at O and a radius of 6 feet. What is the height h, in feet, of the archway 2 feet from its center?
A. √2
B. 2
C. 3
D. 4√2
E. 6
NEW question from GMAT® Official Guide 2019
(PS05957)
Attachment:
PS05957_f009.jpg
Let's add the radius of 6 feet to the diagram to get:
From here, we can see the right triangle hiding within the diagram, which means we can apply the Pythagorean Theorem.
Se can write: h² + 2² = 6²
Simplify: h² + 4 = 36
So, we get: h² = 32
This means h = √32
Check the answer choices. . . √32 is not among them.
Looks like we need to simplify √32
We'll use the fact that √(xy) = (√x)(√y)
So, √32 = √[(16)(2)] = (√16)(√2) = (4)(√2) = 4√2
Check the answer choices. . . D
Answer: D
Cheers,
Brent
Originally posted by BrentGMATPrepNow on 23 Jun 2018, 09:52.
Last edited by BrentGMATPrepNow on 15 Mar 2020, 05:36, edited 2 times in total.
Last edited by BrentGMATPrepNow on 15 Mar 2020, 05:36, edited 2 times in total.
