GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the right triangle ABC shown above, BDEF is a square.
[#permalink]
28 Jun 2023, 08:16
28 Jun 2023, 08:16
Expert Reply
1
Bookmarks
00:00
Question Stats:
77% (01:31) correct
22% (03:36) wrong based on 9 sessions
Hide Show timer Statistics
Attachment:
GRe right triangle.jpg [ 17.94 KiB | Viewed 1333 times ]
In the right triangle ABC shown above, BDEF is a square.
Quantity A |
Quantity B |
Area of square BDEF |
9 |
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.
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
Re: In the right triangle ABC shown above, BDEF is a square.
[#permalink]
28 Jun 2023, 08:40
28 Jun 2023, 08:40
1
1
Bookmarks
First notice that this is a 45,45, 90 triangle. So the second side will be 6.
We do not know if the square is the midsegement of the legs of the triangle, but nonetheless we can find out its length
Let the sides of the square be x.
That means we have cut the triangle into 3 shapes: the square x, and two triangles - one with base x, and the height (6-x) and another with height x and base 6-x.
The area of the triangle is simply given by (1/2)(6^2)=18.
Knowing the area of the big triangle, we know that the 3 shapes inside must equal the same area.
Therefore:
\(18=0.5(6-x)(x)+0.5(x)(6-x)+x^2\) (area of two triangles+square)
\(18=(6-x)(x)+x^2\)
Now, becuase this is a quantity comparison question we can simply use the answers - QB is 9. So if the area of the square were 9, that implies that x is 3. If the resulting sum is less than 18, that means x is greater than 3 and QA must be bigger. If the resulting sum is equal, then they are the same, and if the resulting sum is greater than 18 x must be smaller than 3 so QB is bigger.
\(18=(6-3)(3)+3^2=3*3+3^2=9+9=18\)
We get 18 on the dot, so that means that x is 3, and the two quantities must be the same.
C
We do not know if the square is the midsegement of the legs of the triangle, but nonetheless we can find out its length
Let the sides of the square be x.
That means we have cut the triangle into 3 shapes: the square x, and two triangles - one with base x, and the height (6-x) and another with height x and base 6-x.
The area of the triangle is simply given by (1/2)(6^2)=18.
Knowing the area of the big triangle, we know that the 3 shapes inside must equal the same area.
Therefore:
\(18=0.5(6-x)(x)+0.5(x)(6-x)+x^2\) (area of two triangles+square)
\(18=(6-x)(x)+x^2\)
Now, becuase this is a quantity comparison question we can simply use the answers - QB is 9. So if the area of the square were 9, that implies that x is 3. If the resulting sum is less than 18, that means x is greater than 3 and QA must be bigger. If the resulting sum is equal, then they are the same, and if the resulting sum is greater than 18 x must be smaller than 3 so QB is bigger.
\(18=(6-3)(3)+3^2=3*3+3^2=9+9=18\)
We get 18 on the dot, so that means that x is 3, and the two quantities must be the same.
C
gmatclubot
Re: In the right triangle ABC shown above, BDEF is a square. [#permalink]
28 Jun 2023, 08:40
Moderators:
