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705-805 (Hard)|   Geometry|      
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GMATBusters
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 01 Aug 2019, 02:21
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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75% (hard)

Question Stats:

34% (01:22) correct 66% (00:58) wrong based on 132 sessions

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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the area of the circle?
A. cannot be determined
B. 10 pi
C. 15 pi
D. 20 pi
E. 25 pi

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A
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DeeptiManyaExpert
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 01 Aug 2019, 22:55
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Hi,

This problem could have been solved, if we knew that the sides 6 and 8 are the legs of the right angled triangle. But, since that is is not mentioned, the answer can not be determined.

Hence, the answer is (A).

This answer is very rare on the GMAT.
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 01 Aug 2019, 23:02
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Hi
You are right that "Can not be determined" option is generally not correct in PS Question, But we must be aware that it can be correct also. So We must read all the options with an open mind.

DeeptiManyaExpert
Hi,

This problem could have been solved, if we knew that the sides 6 and 8 are the legs of the right angled triangle. But, since that is is not mentioned, the answer can not be determined.

Hence, the answer is (A).

This answer is very rare on the GMAT.
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 01 Aug 2019, 23:08
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gmatbusters

Yes, that's the whole point. Double-check all the info before you pick this answer.
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 02 Aug 2019, 05:53
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Hi,

I'm wondering how we can determine the area of a circle equals to 10pi?
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 02 Aug 2019, 07:18
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Hi,

I'm wondering how we can determine the area of a circle equals to 10pi?
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Hi DarleneTran,
Its NOT 10\(\pi\) its " Cannot be determined ", you probably got confused with option B.
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 31 Jul 2020, 20:53
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the area of the circle?
A. cannot be determined
B. 10 pi
C. 15 pi
D. 20 pi
E. 25 pi

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GMATBusters: Kindly recheck the OA as you have mentioned that the triangle is a right angle triangle with sides 6 and 8.

Radius of the circle will be half the hypotenuse. Hence, r = 5

Area = 25 pi

OA to be E.

Smilar Question: https://gmatclub.com/forum/the-lengths- ... fl=similar
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 02 Aug 2020, 09:20
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Hi

you have fallen into the trap.

if in a right-angled triangle, two sides are 6 and 8, it doesn't mean the third side = 10.
the third side can be \(\sqrt{64-36} = \sqrt{28} \)also.

Actually it depends on which sides are 6,8.
if 6 and 8 are the perpendicular sides, the Hypotenuse = 10.
if 8 is the hypotenuse, then the third side = \(\sqrt{28}\)
So, the answer is A.

Happy Learning

nkme2007
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the area of the circle?
A. cannot be determined
B. 10 pi
C. 15 pi
D. 20 pi
E. 25 pi

GMATbuster's Collection

GMATBusters: Kindly recheck the OA as you have mentioned that the triangle is a right angle triangle with sides 6 and 8.

Radius of the circle will be half the hypotenuse. Hence, r = 5

Area = 25 pi

OA to be E.

Smilar Question: https://gmatclub.com/forum/the-lengths- ... fl=similar
Show more
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nkme2007
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GMAT 1: 670 Q50 V31
GPA: 4
WE:Project Management (Real Estate)
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Schools: IIMB EPGP'22 (M)
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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 02 Aug 2020, 09:24
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GMATBusters
Hi

you have fallen into the trap.

if in a right-angled triangle, two sides are 6 and 8, it doesn't mean the third side = 10.
the third side can be \(\sqrt{64-36} = \sqrt{28} \)also.

Actually it depends on which sides are 6,8.
if 6 and 8 are the perpendicular sides, the Hypotenuse = 10.
if 8 is the hypotenuse, then the third side = \(\sqrt{28}\)
So, the answer is A.

Happy Learning

nkme2007
GMATBusters
The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the area of the circle?
A. cannot be determined
B. 10 pi
C. 15 pi
D. 20 pi
E. 25 pi

GMATbuster's Collection

GMATBusters: Kindly recheck the OA as you have mentioned that the triangle is a right angle triangle with sides 6 and 8.

Radius of the circle will be half the hypotenuse. Hence, r = 5

Area = 25 pi

OA to be E.

Smilar Question: https://gmatclub.com/forum/the-lengths- ... fl=similar
Show more

Yah.. Correct.

Thank You.

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The lengths of two sides in a right-angle triangle are 6 cm and 8 cm. 09 Aug 2020, 22:19
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Option E: 25 PI is correct because if hypotenuse of the triangle would have been 8 than area of the circle would have been 16 pi, hypotenuse would have become the diameter of the triangle but no such option is present.
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