A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what

(d1^2 + d2^2) = 2(l1^2 + l2^2)

Substitute d1 = 16, l1 = 18, l2 = 14

d2 = 28 (answer)

Is the answer 28?

I used the formula d1^2 + d2^2 =2(a^2+b^2)

where d1 and d2 are the two diagonals and a and b are the two sides.

Is this a GMAT question?

OA is 28
Nice gayathri. I just wanted to bring up this formula as it could be useful. You just never know, the GMAT is full of surprises.

it is useful concept to all. therefore, i thought it is useful to bring it into the discussion.

Sum of the square of Diagnals of parallogram = D1^2 + D2^2 = 2 (a^2 + b^2), Where D1 and D2 are the two diagonals and a and b are the two different sides of the parallogram.

Length of the second diagnol is 44.

Area(parallelogram)=18X14=252/2=176 (Area of each triangle)

Base/2Xheight=Area(triangles)

16/2XH=176

H=22

22X2=44

It's a very good question.
lets a and b - sides
d1 and d2 diagonals
The key formular is:
d1^2+d2^2=2*(a^2+b^2).

from that another digonal is 28 ( if I'm not mistaken in calculations).

Difficult to describe.

Draw a big rectangle on a sheet of paper.
Its height is y.
Its length is 18+x.
On the top mark x from the left.
On the bottom mark x from the right.
Draw in the parallelogram inscribed within this rectangle.
(By drawing line from bottom left corner to point on top x from left.)
Mark a rectangle on the left, which is x wide, y high.
The diagonal is 14. Side of parallelogram.

So x^2 + y^2 = 14^2 = 196 (E1)

Let z = 18 - x (E2), z is the middle width portion of the rectangle.

Then you can split the bottom line, into three parts,
x, z, x.
Now we know the length of the shorter diagonal 16.
But this is the hypotenuse of a triangle.
The sides are y and z.

So y^2 + z^2 = 16^2 = 256 (E3)

(E3) - (E1)
z^2 - x^2 = 60
From (E2) z = 18 - x
So z^2 = 18^2 - 36x + x^2

(324 - 36x + x^2) - x^2 = 60
(324 - 60) = 36x
x = 264 / 36 = 22 / 3

Hence (E2)
z = 18 - 22/3 = 32/3

And (E1)
y^2 = 196 - x^2 = 196 - (22/3)^2
y^2 = (1764 - 484) / 9 = 1280/9

Width of rectangle,
w = 18 + x = (54+22)/3 = 76/3

Diagonal d
d^2 = w^2 + y^2
d^2 = (76^2)/9 + 1280/9
d^2 = (5776+1280)/9 = 7056/9
d = 84/3 = 28

But there would not be time to do this in the real GMAT.

I too was wondering where from this new formula came. A little trignometry helped derive formula though. Anyone interested in derivation can look into attached doc.

For others, get this formula in your kitty.