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.
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 in^{2}
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
-7x = 21 -x = 21/7 -x = 3 x = -3 |
2y = 10 y = 10/2 y = 5 |
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
27 = 63 – 6x 27 – 63 = - 6x -36 = -6x x = 6 |
4 + y = 15 y = 15 - 4 y =11 |
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
64 = 19 + 5x 64 – 19 = 5x 45 = 5x 9 = x |
3y – 3 = 72 3y = 72 + 3 3y = 75 y = 25 |
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
18 = -x + 7 18 – 7 = - x -11 = x |
36 = 6y (36)/6 = y 6 = y |
Therefore, x = -11 and y = 6.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM