# HOW TO FIND THE LENGTH OF DIAGONAL OF A PARALLELOGRAM

Definition of parallelogram :

A parallelogram is a quadrilateral which has opposite sides parallel.

Properties of parallelogram :

• Opposite sides are equal in length
• Opposite angles are equal in size.
• Diagonals bisect each other.
• Consecutive interior angles add upto 180.

Problem 1 :

For the parallelogram given below, solve for m and n.

Solution :

Since the given shape is a parallelogram, the diagonals will bisect each other.

 AO = OCm + 8 = 3m ---(1)8 = 3m - m2m = 8m = 4 BO = OD9 = 2n - 12n = 9 + 12n = 10n = 5

Problem 2 :

For the parallelogram given below, solve for j and k.

Solution :

 AO = COk + 10 = 6k6k - k = 105k = 10k = 2 BO = OD5j - 9 = 3j5j - 3j = 92j = 9j = 4.5

Problem 3 :

In parallelogram PQRS, solve for x and y.

Solution :

 QT = ST2x + 8 = 182x = 18 - 82x = 10x = 10/2x = 5 PT = TR4y - 2 = 224y = 22 + 24y = 24y = 24/4y = 6

Problem 4 :

Solve the n in the following parallelogram ABCD. Find length of the diagonal BD.

Solution :

Diagonals will bisect each other.

3n - 6 = 5n - 122

3n - 5n = -122 + 6

-2n = -116

Dividing by 2 on both sides.

n = 116/2

n = 58

Length of BD = 3n - 6 + 5n - 122

= 8n - 128

= 8(58) - 128

= 464 - 128

= 336

So, length of the diagonal BD is 336.

Problem 5 :

Length of the longer diagonal in the parallelogram FAST.

Solution :

FO = 5.5, then FS = 5.5(2) ==>  11

TO = 3x - 1, OA = 2x + 7

3x - 1 = 2x + 7

3x - 2x = 7 + 1

x = 8

Length of diagonal TA = 3x - 1 + 2x + 7

= 5x + 6

= 5(8) + 6

= 40 + 6

= 46

So, length of the longer diagonal is 46.

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