In a parallelogram ABCD, If AB = 2x + 5, CD = y + 1, AD = y + 5 and BC = 3x - 4, then ratio AB:BC is
Question
Solution
In a parallelogram, opposite sides are equal. Therefore, we can equate AB to CD and AD to BC.
So, we have:
2x + 5 = y + 1 ----(1)
and
y + 5 = 3x - 4 ----(2)
We can solve these two equations to find the values of x and y.
From equation (1), we can express y in terms of x:
y = 2x + 5 - 1 y = 2x + 4
Substitute y = 2x + 4 into equation (2):
2x + 4 + 5 = 3x - 4 2x + 9 = 3x - 4 9 + 4 = 3x - 2x 13 = x
Substitute x = 13 into y = 2x + 4:
y = 2*13 + 4 y = 26 + 4 y = 30
So, the values of x and y are 13 and 30 respectively.
Now, we can find the ratio AB:BC.
AB = 2x + 5 = 213 + 5 = 31 BC = 3x - 4 = 313 - 4 = 35
Therefore, the ratio AB:BC is 31:35.
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