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In a parallelogram ABCD, if AB = 2x+5,CD = y+1, AD= y+5 and BC = 3x−4,what is the ratio of AB and BC?
- a)71:21
- b)12:11
- c)31:35
- d)4:7
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a parallelogram ABCD, ifAB = 2x+5,CD= y+1,AD= y+5andBC = 3x−4...
We know that in a parallelogram opposite sides are equal.
∴ AB = CD or 2x+5=y+1 and AD = BC or y+5=3x−4
2x−y =−4 ....(i)
y−3x = −9 .....(ii) Adding (i) and (ii), we get −x =−13 or x = 13
2x−y =−4 ....(i)
y−3x = −9 .....(ii) Adding (i) and (ii), we get −x =−13 or x = 13
and y = 30. Substituting, we have
AB = 31 cm and BC = 35 cm
∴The required ratio = 31:35
∴The required ratio = 31:35
Most Upvoted Answer
In a parallelogram ABCD, ifAB = 2x+5,CD= y+1,AD= y+5andBC = 3x−4...
In a parallelogram, opposite sides are equal in length.
Therefore, AB = CD and AD = BC.
Given that AB = 2x + 5, CD = y + 1, AD = y + 5, and BC = 3x, we can set up two equations:
2x + 5 = y + 1 (equation 1)
y + 5 = 3x (equation 2)
From equation 1, we can isolate y:
y = 2x + 4
Substituting this value of y into equation 2, we get:
2x + 4 + 5 = 3x
Simplifying, we have:
9 = x
Now we can substitute this value of x back into the equations to find the lengths of the sides:
AB = 2(9) + 5 = 23
CD = y + 1 = (2(9) + 4) + 1 = 23
AD = y + 5 = (2(9) + 4) + 5 = 27
BC = 3(9) = 27
So, the lengths of the sides are AB = 23, CD = 23, AD = 27, and BC = 27.
Therefore, AB = CD and AD = BC.
Given that AB = 2x + 5, CD = y + 1, AD = y + 5, and BC = 3x, we can set up two equations:
2x + 5 = y + 1 (equation 1)
y + 5 = 3x (equation 2)
From equation 1, we can isolate y:
y = 2x + 4
Substituting this value of y into equation 2, we get:
2x + 4 + 5 = 3x
Simplifying, we have:
9 = x
Now we can substitute this value of x back into the equations to find the lengths of the sides:
AB = 2(9) + 5 = 23
CD = y + 1 = (2(9) + 4) + 1 = 23
AD = y + 5 = (2(9) + 4) + 5 = 27
BC = 3(9) = 27
So, the lengths of the sides are AB = 23, CD = 23, AD = 27, and BC = 27.
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In a parallelogram ABCD, ifAB = 2x+5,CD= y+1,AD= y+5andBC = 3x−4,what is the ratio of AB and BC?a)71:21b)12:11c)31:35d)4:7Correct answer is option 'C'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In a parallelogram ABCD, ifAB = 2x+5,CD= y+1,AD= y+5andBC = 3x−4,what is the ratio of AB and BC?a)71:21b)12:11c)31:35d)4:7Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a parallelogram ABCD, ifAB = 2x+5,CD= y+1,AD= y+5andBC = 3x−4,what is the ratio of AB and BC?a)71:21b)12:11c)31:35d)4:7Correct answer is option 'C'. Can you explain this answer?.
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