Question

In parallelogram ABCD, AB=(5x+2y) cm, BC=(3x+2y+2) cm, CD=(2x+y+6) cm, AD=(2x+y) cm, then find the length of side AB and side BC.



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Answer 1

Answer :-

• AB = 8 cm
• BC = 2 cm

Solution :-

Given in the Question, ABCD is a Parallelogram in which the side AB = (5x + 2y) cm , BC= (3x + 2y + 2) , CD = (2x + y + 6) cm and AD = (2x + y) cm

As we know, Opposite sides of a Parallelogram are equal.

∴ AB = CD

⇒ 5x + 2y = 2x + y + 6

⇒ 3x + y = 6 ...(1)

Similarly,

⇒ BC = AD [ Opposite sides of a Parallelogram are equal ]

⇒ 3x + 2y + 2 = 2x + y

⇒ x + y = -2 ...(2)

Subtracting (2) from (1), we get

⇒ 3x + y - x - y = 6 - (-2)

⇒ 2x = 6 + 2

⇒ 2x = 8

⇒ x = 4

Substituting [x = 4] in (2)

⇒ 4 + y = -2

⇒ y = -6

We get, x = 4 and y = -6

Now,

Length of side AB = 5x + 2y cm

⇒ AB = 5×4 + 2×-6

⇒ AB = 20 - 12

⇒ AB = 8 cm

Similarly,

Length of side BC = 3x + 2y + 2

⇒ BC = 3×4 + 2×-6 + 2

⇒ BC = 12 - 12 + 2

⇒ BC = 2 cm

Hence, The length of side BC is 2 cm while length of side AB is 8 cm.

Some Properties of a Parallelogram :-

• Opposite sides of a Parallelogram are equal.
• Opposite angles of a Parallelogram are also equal.
• The sum of two Adjacent angles of a Parallelogram is 180° .
• The Diagonals of a Parallelogram bisect each other.
• A diagonal divides the parallelogram into two congruent triangles of equal area.