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Triangle BED

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Triangle BED

by GmatKiss » Tue Nov 01, 2011 3:55 am
How to do approach this one!

OE not satisfactory :(
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by rijul007 » Tue Nov 01, 2011 4:05 am
Area of the shaded region = 1/2 * x * y = 1/2 * y(y+2)

y(y+2) = 48
y = 6

hence x = 8

x^2 + y^2 = z^2
36 + 64 = z^2 = 100
z = 10

Option E
Last edited by rijul007 on Tue Nov 01, 2011 4:12 am, edited 1 time in total.
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by neelgandham » Tue Nov 01, 2011 4:10 am
GmatKiss wrote:How to do approach this one!

OE not satisfactory :(
x=y+2 => x-y =2 -(1)
area of traiangle = 0.5*x*y = 24 => xy = 48 -(2)

From 1 and 2

Z^2 = x^2 + y^2 = ((x-y)^2) +2*x*y = (2^2)+(2*48) = 100 => Z =10 Option E
Last edited by neelgandham on Tue Nov 01, 2011 4:10 am, edited 1 time in total.
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by shankar.ashwin » Tue Nov 01, 2011 4:10 am
The area of a rt. triangle is given.

1/2 * b*h = 24
b*h=48.

Also given 'h' is 2 more than 'b'.
So only possibility is 6 and 8 (6*8 = 48)

Now using phy. theorem find hyp; Sqrt(36+64) = 10 IMO
Last edited by shankar.ashwin on Tue Nov 01, 2011 4:13 am, edited 1 time in total.
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by neelgandham » Tue Nov 01, 2011 4:11 am
rijul007 wrote:Area of the shaded region = 1/2 * x * y = 1/2 * y(y+2)

1/2 * y(y+2) = 24 => y(y+2)=48 and not 24, => y =6 and x = 8 and z =10

y(y+2) = 24
y = -6 or 4

as the value cant be ngative, we take y=4

hence x = 6

x^2 + y^2 = z^2
36 + 16 = z^2 = 52
z = 2*root(13)

Option B
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by rijul007 » Tue Nov 01, 2011 4:13 am
damn,what's happened to me!!

thnks again neelgandham
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by GmatKiss » Tue Nov 01, 2011 4:15 am
shankar.ashwin wrote:The area of a rt. triangle is given.

1/2 * b*h = 24
b*h=48.

Also given 'h' is 2 more than 'b'.
So only possibility is 6 and 8 (6*8 = 48)

Now using phy. theorem find hyp; Sqrt(36+64) = 10 IMO
Nice catch! thanks :)
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by GMATGuruNY » Tue Nov 01, 2011 5:40 am
Image
ALWAYS LOOK AT THE ANSWER CHOICES before you do any math.

Seeing 6, 8 and 10 in the answer choices should make us look for a 6-8-10 triangle.
y=6 and x=8 satisfy the condition that x = y+2.
If x=8 and y=6, then the area = (1/2)*6*8 = 24, satisfying the only other condition given.
Thus, the triangle is a 6-8-10 triangle with a hypotenuse of 10.

The correct answer is E.
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by atnt444 » Wed Nov 02, 2011 8:20 am
I agree with the approach by GMAT guru !! that seems to be the best one !!

This is what I did :

area of triangle = 1/2 B.H => 1/2 (y+2)(y) .
Then looking at the options I could easily tellit has to be 6 and 8(6+2) leading the value of z to be 10 .
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by vaibhavgupta » Wed Nov 02, 2011 8:31 am
GmatKiss wrote:How to do approach this one!

OE not satisfactory :(
E it is! :)
If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A

FML!! :/
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