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The area of ABC
[#permalink]
Updated on: 26 Dec 2018, 11:20
Updated on: 26 Dec 2018, 11:20
Expert Reply
2
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Question Stats:
66% (01:06) correct
33% (01:00) wrong based on 186 sessions
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Attachment:
#GREpracticequestion The area of ABC.jpg [ 18.79 KiB | Viewed 7931 times ]
Quantity A |
Quantity B |
The area of \(\triangle ABC\) |
The area of \(\triangle DEF\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
_________________
Re: The area of ABC
[#permalink]
26 Apr 2017, 11:59
26 Apr 2017, 11:59
3
1
Bookmarks
Triangle ABC is a isosceles right-angled triangle.A = C = 45 degrees.Therefore, AB = BC = Sq.root(2)
Area of triangle ABC = 1/2 * Sq.root(2) * Sq.root(2)
= 1/2 * 2
= 1
In Triangle DEF , angle F= 30 degrees.
Sin 30 = 1/2 =DE/2
DE = 1
Also, Cos 30 = Sq.root(3)/2 = EF/2
EF = Sq.root(3) = 1.732
This implies area of triangle DEF = 1/2 * 1 * 1.732
= .866
Clearly,Area of ABC is greater than Area of DEF.
Area of triangle ABC = 1/2 * Sq.root(2) * Sq.root(2)
= 1/2 * 2
= 1
In Triangle DEF , angle F= 30 degrees.
Sin 30 = 1/2 =DE/2
DE = 1
Also, Cos 30 = Sq.root(3)/2 = EF/2
EF = Sq.root(3) = 1.732
This implies area of triangle DEF = 1/2 * 1 * 1.732
= .866
Clearly,Area of ABC is greater than Area of DEF.
Re: The area of ABC
[#permalink]
29 Sep 2018, 10:27
29 Sep 2018, 10:27
1
Right triangle 1:1:root{2} and 1:root{3}:2....the one with more symmetry will have the higher area.
Re: The area of ABC
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23 Dec 2018, 22:07
23 Dec 2018, 22:07
Do they ask questions based on sin and cos formulas in GRE ?
Re: The area of ABC
[#permalink]
26 Dec 2018, 03:43
26 Dec 2018, 03:43
1
Expert Reply
kunalkmr62 wrote:
Do they ask questions based on sin and cos formulas in GRE ?
No, definitely.
Regards
_________________
Re: The area of ABC
[#permalink]
26 Dec 2018, 22:49
26 Dec 2018, 22:49
1
Expert Reply
kunalkmr62 wrote:
Do they ask questions based on sin and cos formulas in GRE ?
Trigonometry is not tested on GRE or GMAT.
This means there is always another way to do the question..
Here we have two types of triangles..
45-45-90 sides are 1:1:√2 or √2:√2:2..Area = √2*√2*1/2=1=A
30-60-90 sides are 1:√3:2....Area = 1*√3*1/2=√3/2=1.74/2=0.87=B
Thus A>B
_________________
Some useful Theory.
1. Arithmetic and Geometric progressions : https://gre.myprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://gre.myprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://gre.myprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://gre.myprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://gre.myprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
1. Arithmetic and Geometric progressions : https://gre.myprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://gre.myprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://gre.myprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://gre.myprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://gre.myprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
Re: The area of ABC
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11 Jan 2019, 15:16
11 Jan 2019, 15:16
kunalkmr62 wrote:
Do they ask questions based on sin and cos formulas in GRE ?
no.
Re: The area of ABC
[#permalink]
21 Jul 2023, 08:22
21 Jul 2023, 08:22
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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