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The area of ABC

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The area of ABC [#permalink] New post 26 Apr 2017, 02:39
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Question Stats:

55% (00:54) correct 44% (01:10) wrong based on 56 sessions


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Quantity A
Quantity B
The area of ABC
The area of 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.
[Reveal] Spoiler: OA

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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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Re: The area of ABC [#permalink] New post 29 Sep 2018, 10:27
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   [#permalink] 29 Sep 2018, 10:27
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The area of ABC

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