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

Question

https://gmatclub.com/forum/download/file.php?id=40820 What is the perimeter of the triangle shown? (1) The area of the triangle is 96 in^2. (2) y = x + 4 2018-04-13_1227.png

Hatakekakashi · Answer

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

Princ · Answer

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

GMATBusters · Answer

This question can be easily be done by busters graphical approach.

push12345 · Answer

I)area of ∆ =96
x*y/2=96
x*y=2^6*3

There can be number of values which x and y can take but only values 16 and 12 will square up to give 400
So sufficient

II)x^2 +(x+4)^2=400
Solving equation we get unique value of x as 12 and y as 16 so
Sufficient

Ans D

Posted from my mobile device

NonPlus · Answer

I guess there is no need to solve any equation.
To find out the perimeter, we need to find the values of 'x' and 'y'. To solve this, we need to have 2 equations (to calculate values of 'n' number of variables, we need 'n' equations).
We can deduce 1 equation from figure itself i.e. x^2 + y^2 = 400 (From pythagoras theorem) and we need to deduce 2nd one now.

(a) Area of triangle is 96.
 Hence, (1/2)*x*y = 96. (2nd equation)
(b) y = x + 4 (2nd equation)

So, we can get an equation from either of these options, leading us to mark answer 'D'

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

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