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# What is the perimeter of triangle ABC?

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
What is the perimeter of triangle ABC?  [#permalink]

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17 Jan 2019, 23:53
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:24) correct 12% (02:01) wrong based on 31 sessions

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What is the perimeter of triangle ABC?

A 44
B 45
C 54
D 60
E 96

Attachment:

2019-01-18_1051.png [ 6.92 KiB | Viewed 409 times ]

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Joined: 11 Jan 2018
Posts: 7
Re: What is the perimeter of triangle ABC?  [#permalink]

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18 Jan 2019, 00:33
Using pythagorean theorem, we can calculate the sides- AB&DC :
to find the parameter of triangle ABC.
In Triangle ABD:
(AB)^sq= (9)^sq + (12)^sq
(AB)^sq= 81 + 144
(AB)^sq= 225..
Taking square roots both sides:
AB= +15, -15.. ( Since side of a triangle can not be negative,so value "-15" is not considered.
Therefore AB= 15.......(1)

Similarly in triangle BDC:
(BC)^sq= (BD)^sq + (DC)^sq
(DC)^sq = (BC)^sq - (DC)^sq
(DC)^sq = (20)^sq - (12)^sq
(DC)^sq = 400 - 144
(DC)^sq = 256
Taking square roots both sides:
DC= +16, -16.. ( Since side of a triangle can not be negative,so value "-16" is not considered.
Therefore DC= 16

Therefore AC= 9+16= 25....(2)

Parameter of Triangle ABC: AB+BC+AC
Side AB= 15, BC=20, AC=25
So, Parameter = 15+20+25 =60

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Re: What is the perimeter of triangle ABC?  [#permalink]

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18 Jan 2019, 06:19
1
Bunuel wrote:

What is the perimeter of triangle ABC?

A 44
B 45
C 54
D 60
E 96

Attachment:
2019-01-18_1051.png

solve <30 seconds
use triangel rule 3:4:5
we see sides are base 9,16,15 & 20
sum = 60
IMO D
Re: What is the perimeter of triangle ABC?   [#permalink] 18 Jan 2019, 06:19
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