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D
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Difficulty:
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57%
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based on 88
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In the figure below, the rectangular at the corner measures 10cm x 20cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?
A) 10
B) 40
C) 30
D) 50
E) None of the above
A) 10
B) 40
C) 30
D) 50
E) None of the above
Attachment:
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03 Mar 2015, 06:27
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ynaikavde
Consider the diagram below:
(r - 10)^2 + (r - 20)^2 = r^2;
r = 10 or r = 50.
r cannot be 10, so it's 50.
Answer: D.
Attachment:
Untitled.png [ 5.81 KiB | Viewed 39842 times ]
Updated on: 23 May 2020, 06:17
Originally posted by BrentGMATPrepNow on 20 Nov 2016, 07:11.
Last edited by BrentGMATPrepNow on 23 May 2020, 06:17, edited 1 time in total.
Last edited by BrentGMATPrepNow on 23 May 2020, 06:17, edited 1 time in total.
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A) 10
B) 40
C) 30
D) 50
E) None of the above
Notice that, once Bunuel creates the equation (r - 10)² + (r - 20)² = r², he doesn't try to solve it (a fair bit of work).
Instead, he starts plugging in the answer choices.
As he's doing that, he's looking for variations of some common Pythagorean triples. These are possible INTEGERS lengths that are possible in a right triangles.
The 4 most common Pythagorean triples are:
3-4-5
5-12-13
8-15-17
7-24-25
You'll see that each of these triples satisfies the Pythagorean Theorem (a² + b² = c²)
For example, 3² + 4² = 5² AND 5² + 12² = 13², etc)
So, when he plugs answer choice D (r = 50) into his equation (r - 10)² + (r - 20)² = r² he gets: (50 - 10)² + (50 - 20)² = 50²
Simplify to get: 40² + 30² = 50²
PERFECT, this is a variation of 3² + 4² = 5², but in this instance, each side is 10 times the length of the 3-4-5 right triangle.
As such, Bunuel automatically know that r = 50 is a solution to his equation.
B) 40
C) 30
D) 50
E) None of the above
Bunuel
Notice that, once Bunuel creates the equation (r - 10)² + (r - 20)² = r², he doesn't try to solve it (a fair bit of work).
Instead, he starts plugging in the answer choices.
As he's doing that, he's looking for variations of some common Pythagorean triples. These are possible INTEGERS lengths that are possible in a right triangles.
The 4 most common Pythagorean triples are:
3-4-5
5-12-13
8-15-17
7-24-25
You'll see that each of these triples satisfies the Pythagorean Theorem (a² + b² = c²)
For example, 3² + 4² = 5² AND 5² + 12² = 13², etc)
So, when he plugs answer choice D (r = 50) into his equation (r - 10)² + (r - 20)² = r² he gets: (50 - 10)² + (50 - 20)² = 50²
Simplify to get: 40² + 30² = 50²
PERFECT, this is a variation of 3² + 4² = 5², but in this instance, each side is 10 times the length of the 3-4-5 right triangle.
As such, Bunuel automatically know that r = 50 is a solution to his equation.
