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In the given isosceles triangle, if AB = BC = 2 and x = 30°, what is t
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01 Jun 2021, 00:19
01 Jun 2021, 00:19
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In the given isosceles triangle, if AB = BC = 2 and x = 30°, what is the area of the triangle?
A. √3/2
B. 1
C. √3
D. 2
E. 2√3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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In the given isosceles triangle, if AB = BC = 2 and x = 30°, what is t
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02 Jun 2021, 04:37
02 Jun 2021, 04:37
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Carcass wrote:
In the given isosceles triangle, if AB = BC = 2 and x = 30°, what is the area of the triangle?
A. √3/2
B. 1
C. √3
D. 2
E. 2√3
Drop a perpendicular from BD to AC
We now have two identical 30-60-90 triangles ABD and CBD
In 30-60-90 triangle, the ratio of sides is \(x : \sqrt{3}x : 2x\)
We know, AB = BC = \(2 = 2x\)
i.e. \(x = 1\)
Therefore, BD = 1 and AD = CD = \(\sqrt{3}\) and
Area of triangle ABC = \(\frac{1}{2}(AC)(BD) = \frac{1}{2}(2\sqrt{3})(1) = \sqrt{3}\)
Hence, option C
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Re: In the given isosceles triangle, if AB = BC = 2 and x = 30°, what is t
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02 Jun 2021, 11:52
02 Jun 2021, 11:52
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Carcass wrote:
In the given isosceles triangle, if AB = BC = 2 and x = 30°, what is the area of the triangle?
A. √3/2
B. 1
C. √3
D. 2
E. 2√3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Since we're told that AB = BC, we know that the triangle is an isosceles triangle, which means ∠BCA = 30°
So if we draw in the altitude from point B, we get two identical right triangles.
Also notice that these right triangles are both special 30-60-90 right triangles
So let's compare these triangles with our base 30-60-90 right triangle
When we do this, we see that the two red right triangles are identical to the base triangle
So, we can add the following measurements to our diagram:
At this point we're ready to find the area of the triangle.
Area of triangle = (base)(height)/2
So, the area \(= \frac{(\sqrt{3}+\sqrt{3})(1)}{2}= \frac{(2\sqrt{3})(1)}{2}=\sqrt{3}\)
Answer: C
Cheers,
Brent
