Question

AB = x + 8

Answer 1

Answer: The length of BC is 7

Step-by-step explanation: Assuming the lengths of the opposite sides of the quadrilateral are congruent, then

AB=DC and

AD=BC

Inputting the values of AB, DC and AD as given in the question:

x + 8 = 3x ...(1)

x + 3=? ...(2)

We have to solve for the value of x to get the actual lengths and thus ascertain BD.

From equation (1):

8 = 3x - x

8 = 2x

8/2 = x

Therefore, x = 4.

If x = 4 then equation(2) would be

4 + 3= 7.

Hence, the actual lengths of the quadrilateral are:

AB = 4 + 8. DC = 3(4)

=12. =12.

AD = 4 + 3. AD = BC

= 7. Therefore, BC = 7.

Hence, it is confirmed that quadrilateral ABCD is a parallelogram since both the opposite sides are proven to be congruent.