Question

PLEASE HELP ME/
AB = 2x
DC = x + 17
AD = x + 10
BC = ?
Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs. What is the length of BC?
A) 7
B) 17
C) 27
D) 34

Answer 1

Option C:

Length of BC = 27

Solution:

Given lengths of the sides are:

AB = 2x, DC = x + 17, AD = x + 10, BC = ?

Quadrilateral ABCD is a parallelogram.

In parallelogram, opposite sides are congruent.

AB = DC and BC = AD

Let us first find x:

AB = DC

⇒ 2x = x + 17

⇒ 2x – x = 17

⇒ x = 17

Let us find AD:

⇒ AD = x + 10

⇒       = 17 + 10

⇒ AD = 27

We know that, opposite sides are congruent.

BC = AD

BC = 27

Option C is the correct answer.

Hence length of BC = 27.