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655-705 (Hard)|   Geometry|      
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gmatophobia
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What are the sides of a right angled triangle? 09 Nov 2022, 08:02
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C
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Difficulty:

55% (hard)

Question Stats:

57% (01:57) correct 43% (01:58) wrong based on 56 sessions

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What are the sides of a right angled triangle?

1) The difference between hypotenuse and base is 6 cm.

2) The difference between hypotenuse and perpendicular is 3 cm.
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C
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rajtare
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What are the sides of a right angled triangle? 09 Nov 2022, 15:07
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gmatophobia
What are the sides of a right angled triangle?

1) The difference between hypotenuse and base is 6 cm.

2) The difference between hypotenuse and perpendicular is 3 cm.
Show more

let p= perpendicular
b=base
h= hypotenuse
tan90 = p/b
sqrt(3) = p/b
or p=sqrt(3)*b

1) h-b=6
or h=6+b
also h^2 = p^2+b^2
therefore, (b+6)^2 = (sqrt(3)*b)^2 +b^2
b^2+36b+12b= 4b^2
or b^2-4b-12=0
or b(b-6)+2(b-6)
or b=6, or b=-2, since b=-2 not possible

thus we can calculate other unique values of other variables hence Sufficient

2) h-p=3
or h=p+3
(p+3)^2 = (p/sqrt(3))^2+ p^2
3(p^2+9+6p)= p^2 +3p^2
or p^2-18p-27-0
solving for P we get two possible values of p, hence not sufficient

Thus correct Answer should be A.
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What are the sides of a right angled triangle? 09 Nov 2022, 23:41
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rajtare
gmatophobia
What are the sides of a right angled triangle?

1) The difference between hypotenuse and base is 6 cm.

2) The difference between hypotenuse and perpendicular is 3 cm.

let p= perpendicular
b=base
h= hypotenuse
tan90 = p/b
sqrt(3) = p/b
or p=sqrt(3)*b

1) h-b=6
or h=6+b
also h^2 = p^2+b^2
therefore, (b+6)^2 = (sqrt(3)*b)^2 +b^2
b^2+36b+12b= 4b^2
or b^2-4b-12=0
or b(b-6)+2(b-6)
or b=6, or b=-2, since b=-2 not possible

thus we can calculate other unique values of other variables hence Sufficient

2) h-p=3
or h=p+3
(p+3)^2 = (p/sqrt(3))^2+ p^2
3(p^2+9+6p)= p^2 +3p^2
or p^2-18p-27-0
solving for P we get two possible values of p, hence not sufficient

Thus correct Answer should be A.
Show more

How did you get the relation that p/b=sqrt(3)? We have not been given any info about the angle opposite to the Perpendicular side.
IMO, the answer should be C because there are three variables(sides) and with each statement, only 2 equations can be formed:
1. Using the Pythagorean Theorem.
2. Using the statement.
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rajtare
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What are the sides of a right angled triangle? 10 Nov 2022, 00:59
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AbhiPathania
rajtare
gmatophobia
What are the sides of a right angled triangle?

1) The difference between hypotenuse and base is 6 cm.

2) The difference between hypotenuse and perpendicular is 3 cm.

let p= perpendicular
b=base
h= hypotenuse
tan90 = p/b
sqrt(3) = p/b
or p=sqrt(3)*b

1) h-b=6
or h=6+b
also h^2 = p^2+b^2
therefore, (b+6)^2 = (sqrt(3)*b)^2 +b^2
b^2+36b+12b= 4b^2
or b^2-4b-12=0
or b(b-6)+2(b-6)
or b=6, or b=-2, since b=-2 not possible

thus we can calculate other unique values of other variables hence Sufficient

2) h-p=3
or h=p+3
(p+3)^2 = (p/sqrt(3))^2+ p^2
3(p^2+9+6p)= p^2 +3p^2
or p^2-18p-27-0
solving for P we get two possible values of p, hence not sufficient

Thus correct Answer should be A.

How did you get the relation that p/b=sqrt(3)? We have not been given any info about the angle opposite to the Perpendicular side.
IMO, the answer should be C because there are three variables(sides) and with each statement, only 2 equations can be formed:
1. Using the Pythagorean Theorem.
2. Using the statement.
Show more
I'm using value of tan(90) = sqrt(3) = p/b to get the relation between perpendicular and base. I'm using tan(90) as its a right angle triangle.

I hope it helps.
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What are the sides of a right angled triangle? 10 Nov 2022, 01:10
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rajtare
gmatophobia
What are the sides of a right angled triangle?

1) The difference between hypotenuse and base is 6 cm.

2) The difference between hypotenuse and perpendicular is 3 cm.

let p= perpendicular
b=base
h= hypotenuse
tan90 = p/b
sqrt(3) = p/b
or p=sqrt(3)*b

1) h-b=6
or h=6+b
also h^2 = p^2+b^2
therefore, (b+6)^2 = (sqrt(3)*b)^2 +b^2
b^2+36b+12b= 4b^2
or b^2-4b-12=0
or b(b-6)+2(b-6)
or b=6, or b=-2, since b=-2 not possible

thus we can calculate other unique values of other variables hence Sufficient

2) h-p=3
or h=p+3
(p+3)^2 = (p/sqrt(3))^2+ p^2
3(p^2+9+6p)= p^2 +3p^2
or p^2-18p-27-0
solving for P we get two possible values of p, hence not sufficient

Thus correct Answer should be A.
Show more

Few issues in here -

1) This question can be solved without trigonometry.
2) Tan 90 is not \(\sqrt{3}\) , the value of tan 90 is undefined.

Show Spoiler
How ? tan 90 = \(\frac{ sin 90 }{ cos 90}\) = \(\frac{1}{0}\) = undefined
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What are the sides of a right angled triangle? 10 Nov 2022, 01:15
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rajtare, If you mean tan(90 degrees), that is an undefined value in math. tan(60 degrees) is equal to sqrt(3) but it is not mentioned anywhere that the angle opposite to Perpendicular side is 60 degrees. Am I missing something?
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What are the sides of a right angled triangle? 26 Jan 2023, 06:26
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Assuming:
x = perpendicular
z = base
y = hypotenuse

a. y-z=6 doesn't give us anything about x. INSUFFICIENT.
b. y-x=3 doesn't give us anything about z. INSUFFICIENT.
c. arranging the equation, we get:
x=y-3
z=y-6
since it's a right triangle, we can use the pythagorean theorem to solve for y.
(y-3)^2 + (y-6)^2 = y^2
SUFFICIENT. Answer is C.
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