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# Triangle ABC is symmetric about the y-axis. Point A is located at (-4,

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Math Expert
Joined: 02 Sep 2009
Posts: 55236
Triangle ABC is symmetric about the y-axis. Point A is located at (-4,  [#permalink]

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19 Jul 2017, 23:31
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Difficulty:

35% (medium)

Question Stats:

67% (02:28) correct 33% (02:35) wrong based on 28 sessions

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Triangle ABC is symmetric about the y-axis. Point A is located at (-4,0), and AB is the longest side of ABC. If the perimeter of ABC is 18, what is the area?

A. 3√2
B. 6
C. 6√2
D. 12
E. 24

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Joined: 19 May 2017
Posts: 2
Re: Triangle ABC is symmetric about the y-axis. Point A is located at (-4,  [#permalink]

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20 Jul 2017, 02:41
one co-ordinate of the triangle is (4,0) so the horizontally opposite co-ordinate is (4,0) as the triangle is symmetrical about y-axis.
length of this line of triangle is 4-(-4) = 8.
as the perimeter is 18, sum of remaining two sides = 10 and so the length of each side is 5
if we consider half part of the triangle, it is a right angled triangle with hypotenuse = 5, base = 4 making height = 3

so it is a triangle with height = 3 and base = 8, hence area = 1/2 * 8 * 3 = 12 ... option D
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Joined: 05 Mar 2015
Posts: 998
Re: Triangle ABC is symmetric about the y-axis. Point A is located at (-4,  [#permalink]

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20 Jul 2017, 08:24
Anushree15 wrote:
one co-ordinate of the triangle is (4,0) so the horizontally opposite co-ordinate is (4,0) as the triangle is symmetrical about y-axis.
length of this line of triangle is 4-(-4) = 8.
as the perimeter is 18, sum of remaining two sides = 10 and so the length of each side is 5
if we consider half part of the triangle, it is a right angled triangle with hypotenuse = 5, base = 4 making height = 3

so it is a triangle with height = 3 and base = 8, hence area = 1/2 * 8 * 3 = 12 ... option D

Agreed with D

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Re: Triangle ABC is symmetric about the y-axis. Point A is located at (-4,   [#permalink] 20 Jul 2017, 08:24
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