# Thread: length of the diagonal of a parallelogram?

1. Good post? |

## length of the diagonal of a parallelogram?

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:
SPOILER: 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

2. Good post? |
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

3. Good post? |
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&#176.

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

4. Good post? |
Originally Posted by Dynamo
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?

5. Good post? |
Originally Posted by gibran
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

6. Good post? |
Thanks, Dynamo.

7. Good post? |
C for me.

side =sqrt(d1^2 + d2^2)