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 figure, the diagonal BD of square ABCD is 3.
[#permalink]
31 Jan 2019, 16:37
31 Jan 2019, 16:37
Expert Reply
00:00
Question Stats:
78% (00:52) correct
21% (01:15) wrong based on 123 sessions
Hide Show timer Statistics
Attachment:
#GREpracticequestion In the figure, diagonal BD of square ABCD.jpg [ 9.44 KiB | Viewed 7646 times ]
In the figure, diagonal BD of square ABCD is 3. What is the perimeter of the square?
A) 4.5
B) 12
C) \(3 \sqrt{2}\)
D) \(6 \sqrt{2}\)
E) \(12 \sqrt{2}\)
Re: In the figure, the diagonal BD of square ABCD is 3.
[#permalink]
01 Feb 2019, 08:28
01 Feb 2019, 08:28
1
Solution,
Given,
ABCD is a square. So, all the sides are equal. i.e. AB = BC = CD = DA
Diagonal BD divides the square into two 45-45-90 right triangles.
By the application of Pythagoras theorem,
BD ^ 2 = BC ^ 2 + CD ^ 2
By the calculation, we found,
BD = CD = 3/√2
i.e. AB = BC = CD = DA = 3/√2
Now, Perimeter of a square = 4 * length
= 4 * 3/ √2
= 12 / √2
= 2 * 2 * 3 / √2
= √2 * √ 2 * 2 * 3/ √2
= 6 √2
Thus, the answer is D.
Given,
ABCD is a square. So, all the sides are equal. i.e. AB = BC = CD = DA
Diagonal BD divides the square into two 45-45-90 right triangles.
By the application of Pythagoras theorem,
BD ^ 2 = BC ^ 2 + CD ^ 2
By the calculation, we found,
BD = CD = 3/√2
i.e. AB = BC = CD = DA = 3/√2
Now, Perimeter of a square = 4 * length
= 4 * 3/ √2
= 12 / √2
= 2 * 2 * 3 / √2
= √2 * √ 2 * 2 * 3/ √2
= 6 √2
Thus, the answer is D.
Re: In the figure, the diagonal BD of square ABCD is 3.
[#permalink]
25 Sep 2019, 09:15
25 Sep 2019, 09:15
ARIJOSHI wrote:
Solution,
Given,
ABCD is a square. So, all the sides are equal. i.e. AB = BC = CD = DA
Diagonal BD divides the square into two 45-45-90 right triangles.
By the application of Pythagoras theorem,
BD ^ 2 = BC ^ 2 + CD ^ 2
By the calculation, we found,
BD = CD = 3/√2
i.e. AB = BC = CD = DA = 3/√2
Now, Perimeter of a square = 4 * length
= 4 * 3/ √2
= 12 / √2
= 2 * 2 * 3 / √2
= √2 * √ 2 * 2 * 3/ √2
= 6 √2
Thus, the answer is D.
Given,
ABCD is a square. So, all the sides are equal. i.e. AB = BC = CD = DA
Diagonal BD divides the square into two 45-45-90 right triangles.
By the application of Pythagoras theorem,
BD ^ 2 = BC ^ 2 + CD ^ 2
By the calculation, we found,
BD = CD = 3/√2
i.e. AB = BC = CD = DA = 3/√2
Now, Perimeter of a square = 4 * length
= 4 * 3/ √2
= 12 / √2
= 2 * 2 * 3 / √2
= √2 * √ 2 * 2 * 3/ √2
= 6 √2
Thus, the answer is D.
I think there might be a typo here. I got the following
side length = 3/√2
perimeter = 4 * 3/√2
simplify perimeter by multiplying by 1: (√2/√2)* (12/√2) = 6/√2
