Question

In a parallelogram ABCD if AB=2x+5, CD=y+1, AD=y+5 and BC=3x-4 then ratio of
AB : BC is
A. 71 : 21
B. 12 : 11
C. 31 : 35
D. 4 : 7

Answer 1

Hint: In order to get the right answer we need to use the properties of parallelograms that is opposite sides are equal and parallel and make equations in two variables and then find the value of variables x and y and then put it in the AB and BC and get the ratio. Doing this will solve your problem.

Complete step-by-step answer:

We need to use some of the properties of parallel gram to get this problem solved.
We know that in a parallelogram opposite sides are congruent.

Hence we can say that AB = CD and BC = AD.
Now we can equate their equations as well which are provided in question
2x + 5 = y + 1 and 3x – 4 = y + 5
On solving these equations we will get the new equations as
2x−y=−4......(1)
3x−y=9......(2)
 Now on solving these equations, we will get the value of x=13 and the value of y=30.
 Hence, on putting the values of x and y in AB = 2x + 5 = 2(13) + 5 = 31
BC = 3x−4 = 3(13) − 4 = 35
Hence the ratio AB : BC = 31:35.
So, the correct option is C.

Note: In this problem we have made the equations in two variables with the help of given information and using the properties of parallelogram and then we have solved those equations to get the values of respective variables. And then we have put their values in the terms whose ratio has been asked and found the ratio. Doing this we got the right answer. Some of the properties of parallelogram are its opposite sides are equal and parallel, its diagonals bisects each other at an angle of 90 degrees