Jump to content
Urch Forums

length of the diagonal of a parallelogram?


gibran

Recommended Posts

The four sides of a parallelogram have the same length. What¡¯s the length of one of the diagonals?

1) The side length is 2

2) The length of another diagonal is 2

 

OA:

C

 

 

IMO, it is D.

From (1), the question stem states that the four sides of the parallelogram have the same length. Therefore, length of each side = 2. Now draw a diagonal. We can use Pythagoram theorem to find the length of the diagonal since we know the other 2 sides. Hence suff.

From (2), we know the length of one of the diagonals. Since the diagonals of a parallelogram bisect each other, we can determine the length of the other diagonal.

 

Am I overlooking something in my method of solution? Please advice. Thanks

Link to comment
Share on other sites

As per my knowledge //'s diagonal not necessarily perpendicular to each other. Even if all sides are equal that doesn't mean it will be a reacangle or square as angle may not be right angle.

So Ans should be E.

Correct if I am wrong

Link to comment
Share on other sites

IMO C

 

Question stem says that the parallelogram has equal sides therefore it is either a square or rhombus.

 

Each diagonal of a square and rhombus is the perpendicular bisector of the other. That is, each cuts the other into two equal parts, and they cross and right angles (90°).

 

Statement 1

 

gives us the side but says nothing about it being square or rhombus so the diagonals can differ.... INSUFF

 

Statement 2

 

tells us about one of the diagonals but talks nothing about the sides dimensions....INSUFF

 

together

 

side = 2

 

one of the diagonals = 2

 

therefore

 

(Diag2/2)^2 = 2^2-1^2

 

diag^2 = 12

 

diag = 2*sqrt 3

 

Suff

Link to comment
Share on other sites

IMO C

 

together

 

side = 2

 

one of the diagonals = 2

 

therefore

 

(Diag2/2)^2 = 2^2-1^2

 

diag^2 = 12

 

diag = 2*sqrt 3

 

Suff

 

Didn't understand this part ..... is this ((Diag2/2)^2 = 2^2-1^2) some formula you are using?

Link to comment
Share on other sites

Didn't understand this part ..... is this ((Diag2/2)^2 = 2^2-1^2) some formula you are using?

 

No formula dude!

 

think of a rhombus or a square whose diagonals are perpendicular bisector

 

so the side will be hypotenuse, and half of each diagonal will be legs of the right angle triangle that is formed due to intersection of diagonals.

 

(refer to the attached doc)

 

in this case

 

side = 2

 

half of one diag = 1

 

therefore the other diagonal's half = sqrt(2^2-1^2) = sqrt 3

 

complete diag = 2* sqrt3

 

HTH

Link to comment
Share on other sites

  • 1 month later...

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Restore formatting

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...