SOLVE UNKNOWN VALUES IN EACH PARALLELOGRAM

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length.

In the above figure, ABCD is a Parallelogram.

• If AB ∥ CD, then AB = CD
• If AD ∥ BC, then AD = BC

Find the value of x in each parallelogram.

Problem 1 :

Solution :

By observing the figure,

PQ ∥ RS

So, PQ = RS (Opposite sides of parallel are equal)

Here PQ = x/2 in and RS = 12 in

(x/2) = 12

x = 12 × 2

x = 24 in²

Problem 2 :

Solution :

By observing the figure,

PS ∥ QR

So, PS = QR (Opposite sides of parallel are equal)

Here PQ = 4x ft and RS = 8 ft

4x = 8

x = 8/4

x = 2 ft

Problem 3 :

Solution :

By observing the figure,

PQ ∥ RS

So, PQ = RS (Opposite sides of parallel are equal)

Here PQ = 43 yd and RS = (7 + 3x) yd

43 = (7 + 3x)

Subtracting 7 on both sides.

43 - 7 = 7 + 3x - 7

36 = 3x

36/3 = x

12 yd = x

Problem 4 :

Solution :

By observing the figure,

PS ∥ QR

So, PS = QR (Opposite sides of parallel are equal)

Here PS = 38 in and QR = (x + 43) in

38 = (x + 43)

Subtracting 43 on both sides.

38 - 43 = x + 43 – 43

-5 in. = x

Find the value of x and y in each parallelogram.

Problem 5 :

Solution :

By observing the figure,

PS ∥ QR and PQ ∥ RS

So, PS = QR and PQ = RS (Opposite sides of parallel are equal)

Here PS = (-7x)ft, QR = 21 ft, PQ = (2y)ft, and RS = 10 ft

-7x = 21 and 2y = 10

Therefore, x = -3 and y = 5.

Problem 6 :

Solution :

By observing the figure,

PQ ∥ RS and PS ∥ QR

So, PQ = RS and PS = QR (Opposite sides of parallel are equal)

Here PQ = 27 yd, RS = (63 – 6x) yd, PS = (4 + y) yd, and QR = 15 yd

27 = (63 – 6x) and (4 + y) = 15

Therefore, x = 6 and y = 11.

Problem 7 :

Solution :

By observing the figure,

PS ∥ QR and PQ ∥ RS

So, PS = QR and PQ = RS (Opposite sides of parallel are equal)

Here PS = 64 in, QR = (19 + 5x) in, PQ = (3y - 3) in, and RS = 72 in

64 = (19 + 5x) and (3y – 3) = 72

Therefore, x = 9 and y = 25.

Problem 8 :

Solution :

By observing the figure,

PS ∥ QR and PQ ∥ RS

So, PS = QR and PQ = RS (Opposite sides of parallel are equal)

Here PS = 18 ft, QR = (-x + 7) ft, PQ = 36 ft, and RS = (6y) ft

18 = (-x + 7) and 36 = 6y

Therefore, x = -11 and y = 6.