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The area of ABC
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Carcass
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Joined: 18 Apr 2015
Posts: 21542
The area of ABC [#permalink] New post  Updated on: 26 Dec 2018, 11:20
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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.
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Originally posted by Carcass on 26 Apr 2017, 02:39.
Last edited by Carcass on 26 Dec 2018, 11:20, edited 1 time in total.
Edited by Carcass
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PankajPatel
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Re: The area of ABC [#permalink] New post  26 Apr 2017, 11:59
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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.
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mrr0821
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Joined: 27 Nov 2014
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Re: The area of ABC [#permalink] New post  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.
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kunalkmr62
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Re: The area of ABC [#permalink] New post  23 Dec 2018, 22:07
Do they ask questions based on sin and cos formulas in GRE ?
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Carcass
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Posts: 21542
Re: The area of ABC [#permalink] New post  26 Dec 2018, 03:43
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kunalkmr62 wrote:
Do they ask questions based on sin and cos formulas in GRE ?


No, definitely.

Regards
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chetan2u
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Joined: 01 Nov 2017
Posts: 371
Re: The area of ABC [#permalink] New post  26 Dec 2018, 22:49
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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://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
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AE
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Joined: 09 Nov 2018
Posts: 505
Re: The area of ABC [#permalink] New post  11 Jan 2019, 15:16
kunalkmr62 wrote:
Do they ask questions based on sin and cos formulas in GRE ?

no.
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Re: The area of ABC [#permalink] New post  06 Feb 2021, 23:55
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