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# What is the perimeter of the triangle shown? (1) The area of the tria

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Math Expert
Joined: 02 Sep 2009
Posts: 44655
What is the perimeter of the triangle shown? (1) The area of the tria [#permalink]

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13 Apr 2018, 01:31
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69% (01:09) correct 31% (00:11) wrong based on 16 sessions

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What is the perimeter of the triangle shown?

(1) The area of the triangle is 96 in^2.
(2) y = x + 4

[Reveal] Spoiler:
Attachment:

2018-04-13_1227.png [ 5.79 KiB | Viewed 191 times ]
[Reveal] Spoiler: OA

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Location: India
GMAT 1: 710 Q49 V36
Re: What is the perimeter of the triangle shown? (1) The area of the tria [#permalink]

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13 Apr 2018, 03:21
1
KUDOS
Bunuel wrote:

What is the perimeter of the triangle shown?

(1) The area of the triangle is 96 in^2.
(2) y = x + 4

[Reveal] Spoiler:
Attachment:
2018-04-13_1227.png

1) 1/2xy= 96

xy =192

x^2 + y^2 = 20^2 = 400

(x+y)^2 = x^2+y^2 + 2xy = 400 + 2x192 = 784

(x+y)^2 = 28^2

x+y = 28
xy = 192
using trial and error x=12/16 y=16/12

perimeter can be found

2) y=x+4

X^2 + (x+4)^2 = 20^2

2x^ + 16 + 8x = 400

2x^2 + 8x - 384 = 0

x^2 + 4x - 192 = 0

x^2 + 16 x - 12 x - 192 = 0

X= 12
y = 16

(D) imo
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Joined: 22 Feb 2018
Posts: 79
Re: What is the perimeter of the triangle shown? (1) The area of the tria [#permalink]

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13 Apr 2018, 05:27
Bunuel wrote:

What is the perimeter of the triangle shown?

(1) The area of the triangle is 96 in^2.
(2) y = x + 4

[Reveal] Spoiler:
Attachment:
2018-04-13_1227.png

Given in question
$$x^2+y^2=(20)^2$$
Question ask us to find parameter P,
$$P= 20+x+y$$.
Either finding value of (x+y) or both x and y individually will suffice.

Statement 1 :The area of the triangle is 96 in^2.
Area =$$\frac{x*y}{2}$$
It gives$$xy= 192$$.

Now using $$(x+y)^2=x^2+y^2+2xy$$,$$x^2+y^2=(20)^2$$ and xy= 192, we can get
$$(x+y)^2$$=784
Rejecting -ve value, we get $$(x+y)=28$$
Perimeter can be calculated.
So Statement 1 alone is sufficient

Statement 2 :y = x + 4
Using $$x^2+y^2=(20)^2$$ and y = x + 4, we get
$$x^2+(x+4)^2=(20)^2$$
$$x^2+4x-192=0$$
$$x$$= $$\frac{-4±\sqrt{4^2-4*1*(-192)}}{2*1}$$
$$x=12$$ (Rejecting -ve value of x i.e -16)
Using y = x + 4, we get $$y =16$$
As we know value of x and y individually , Value of perimeter can be easily calculated.
So Statement 2 alone is Sufficient.

As Both Statement are alone sufficient , Answer is D
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Re: What is the perimeter of the triangle shown? (1) The area of the tria [#permalink]

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13 Apr 2018, 06:21
1
KUDOS
This question can be easily be done by busters graphical approach.
Attachments

13_04_2018 18_47 Office Lens.jpg [ 297.74 KiB | Viewed 89 times ]

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Re: What is the perimeter of the triangle shown? (1) The area of the tria   [#permalink] 13 Apr 2018, 06:21
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