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Which is greater AB or 10
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01 Feb 2019, 07:28
01 Feb 2019, 07:28
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Attachment:
#GREpracticequestiuon Which is greater AB or 10.jpg [ 13.46 KiB | Viewed 7656 times ]
Quantity A |
Quantity B |
AB |
10 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: Which is greater AB or 10
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01 Feb 2019, 08:02
01 Feb 2019, 08:02
5
Solution,
Triangle ABC is an isosceles triangle since AC = BC = 10.
IF two sides of a triangle are equal then their corresponding angles are also equal.
So, angle CAB = angle CBA
We know, Sum of the measures of three angles of a triangle = 180°
angle CAB + angle CBA + angle ACB = 180°
angle CAB + angle CBA = 180° - 40° = 140°
i.e. angle CAB = angle CBA = 70°
We know,
In any triangle,
the shortest side is opposite the smallest angle. Here smallest angle = angle ACB = 40°
Hence, side opposite to the smallest angle AC is less than 10
Thus the answer is B.
Triangle ABC is an isosceles triangle since AC = BC = 10.
IF two sides of a triangle are equal then their corresponding angles are also equal.
So, angle CAB = angle CBA
We know, Sum of the measures of three angles of a triangle = 180°
angle CAB + angle CBA + angle ACB = 180°
angle CAB + angle CBA = 180° - 40° = 140°
i.e. angle CAB = angle CBA = 70°
We know,
In any triangle,
the shortest side is opposite the smallest angle. Here smallest angle = angle ACB = 40°
Hence, side opposite to the smallest angle AC is less than 10
Thus the answer is B.
General Discussion
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Re: Which is greater AB or 10
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07 Feb 2019, 15:05
07 Feb 2019, 15:05
3
Carcass wrote:
Attachment:
#GREpracticequestiuon Which is greater AB or 10.jpg
Quantity A |
Quantity B |
AB |
10 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Here's an approach that requires visualization only:
First, to make things easier to see, let's tilt the given diagram so that vertex C is at the top.
So, we have a ISOSCELES triangle with two equal sides of length 10.
In order to answer the question, let's first examine an EQUILATERAL triangle with sides of length 10.
In this case, the length of side AB = 10
Now, if we "grab" the two blue sides and rotate them OUT to create an 80-degree angle at vertex C...
. .. we can see that the length of side AB will be GREATER THAN 10 (which we'll denote as 10+)
Conversely, if we "grab" the two blue sides and rotate them IN to create an 40-degree angle at vertex C...
. .. we can see that the length of side AB will be LESS THAN 10 (which we'll denote as 10-)
If the length of side AB will be LESS THAN 10, then the correct answer is B
Cheers,
Brent
