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

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

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New post 13 Apr 2018, 01:31
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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
2018-04-13_1227.png [ 5.79 KiB | Viewed 191 times ]
[Reveal] Spoiler: OA

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Re: What is the perimeter of the triangle shown? (1) The area of the tria [#permalink]

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New post 13 Apr 2018, 03:21
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Bunuel wrote:
Image
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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Re: What is the perimeter of the triangle shown? (1) The area of the tria [#permalink]

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New post 13 Apr 2018, 05:27
Bunuel wrote:
Image
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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New post 13 Apr 2018, 06:21
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This question can be easily be done by busters graphical approach. :angel:
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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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