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# If the perimeter of right triangle ABC above is 3 + 3, what is the are

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Math Expert
Joined: 02 Sep 2009
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If the perimeter of right triangle ABC above is 3 + 3, what is the are  [#permalink]

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05 Jan 2016, 09:41
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25% (medium)

Question Stats:

70% (01:19) correct 30% (01:37) wrong based on 87 sessions

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If the perimeter of right triangle ABC above is $$3 + 3\sqrt{3}$$, what is the area of the triangle?

(1) AC ≠ AB
(2) angle ABC = 30 °

Attachment:

2016-01-05_2039.png [ 4.47 KiB | Viewed 2057 times ]

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Re: If the perimeter of right triangle ABC above is 3 + 3, what is the are  [#permalink]

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05 Jan 2016, 10:00
1
AB + AC + BC = 3 + 3sqrt(3)

St1: AC is not equal to AB --> Implies angle B and angle C is not equal to 45 deg. But B and C can take any angle other than 45 deg. --> Not sufficient

St2: angle ABC = 30 deg --> It is a 30 60 90 triangle. So, sides are in the ratio 1:sqrt(3):2
Assuming side opposite to 30 deg (AC) is 'a', we will have a + a*sqrt(3) + 2a = 3 + sqrt(3)
Value of a can be found out.
Thus we can obtain the value of AC and AB. Area can be determined.
St2 alone is sufficient.

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If the perimeter of right triangle ABC above is 3 + 3, what is the are  [#permalink]

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05 Jan 2016, 11:24
Bunuel wrote:

If the perimeter of right triangle ABC above is $$3 + 3\sqrt{3}$$, what is the area of the triangle?

(1) AC ≠ AB
(2) angle ABC = 30 °

Attachment:
2016-01-05_2039.png

(1) Ok, this triangle is not isosceles... Zero value. Not sufficient
(2) It's a 90-60-30 Tringle and P $$3 + 3\sqrt{3}$$
$$x+2x+x\sqrt{3}=3 + 3\sqrt{3}$$ --> $$x(3+\sqrt{3})=3 + 3\sqrt{3}$$
x=1, hence we can find all three sides. Answer B
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Re: If the perimeter of right triangle ABC above is 3 + 3, what is the are  [#permalink]

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05 Jan 2016, 12:47
ANS B

Approach:-

Statement 1 - AC\neq{AB} implies the other angles of right angled triangle is not 45 degree and can be any other angle. Clearly not sufficient.

Statement 2 -Angle ABC = 30 , implies standard right angled triangle 30,60,90 and the values, and thus the sides can be calculated using 1:\sqrt{3} : 2. Thus area can be calculated. Sufficient.

Thank you

Bunuel wrote:

If the perimeter of right triangle ABC above is $$3 + 3\sqrt{3}$$, what is the area of the triangle?

(1) AC ≠ AB
(2) angle ABC = 30 °

Attachment:
2016-01-05_2039.png
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Re: If the perimeter of right triangle ABC above is 3 + 3, what is the are  [#permalink]

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21 Mar 2019, 15:17
BrainLab wrote:
(2) It's a 90-60-30 Tringle and P $$3 + 3\sqrt{3}$$
$$x+2x+x\sqrt{3}=3 + 3\sqrt{3}$$ --> $$x(3+\sqrt{3})=3 + 3\sqrt{3}$$
x=1, hence we can find all three sides. Answer B

It should be x=√3, not 1:

x+2x+x√3 = 3+3√3

3x+x√3 = 3+3√3

x(3+1√3) = 3+3√3

√3(3+1√3) = 3+3√3

3√3 + 1*√3*√3 = 3√3+3
Re: If the perimeter of right triangle ABC above is 3 + 3, what is the are   [#permalink] 21 Mar 2019, 15:17
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