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In triangle CAT, the measure of angle A is 90°, the
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27 Aug 2020, 10:28
27 Aug 2020, 10:28
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Question Stats:
61% (01:12) correct
38% (01:27) wrong based on 18 sessions
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In triangle CAT, the measure of angle A is 90°, the length of side CA is 3, and the length of side AT is b. If the length of hypotenuse CT is between 3 and 6, which of the following could be the value of b?
Indicate all such values.
A. 1
B. 2
C. 3
D. 4
E. 5
F. 6
G. 7
Indicate all such values.
A. 1
B. 2
C. 3
D. 4
E. 5
F. 6
G. 7
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Official Answer
A,B,C,D,E
Re: In triangle CAT, the measure of angle A is 90°, the
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27 Aug 2020, 10:29
27 Aug 2020, 10:29
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Re: In triangle CAT, the measure of angle A is 90°, the
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27 Aug 2020, 23:38
27 Aug 2020, 23:38
2
This is an application of Pythagore's theorem.
We have \(CT^2=AC^2 + AT^2\) (because CAT is a right triangle in A)
So \(b^2=CT^2-9\)
But 3<CT<6 so \(9<CT^2<36\)
then \(0<b^2=CT^2-9<27\)
so \(0<b<\sqrt{27}\) which is around 5.19
So we tick all answers below 5.19 that is A,B,C,D,E
We have \(CT^2=AC^2 + AT^2\) (because CAT is a right triangle in A)
So \(b^2=CT^2-9\)
But 3<CT<6 so \(9<CT^2<36\)
then \(0<b^2=CT^2-9<27\)
so \(0<b<\sqrt{27}\) which is around 5.19
So we tick all answers below 5.19 that is A,B,C,D,E
