Question

AB = 44 + 3x BC = 33 + x CD = 64 − x AD = 48 − 2x Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Prove that quadrilateral ABCD is a parallelogram by finding the lengths (in centimeters) of the opposite side pairs?

Answer 1

Given : AB = 44 + 3x

BC = 33 + x

CD = 64 − x

AD = 48 − 2x.

Opposite sides are AB and CD.

BC and AD.

Setting AB equals CD

We get

44 + 3x = 64 − x

Adding x on both sides, we get

44 + 3x+x = 64 − x+x

44 +4x = 64.

Subtracting 44 from both sides, we get

44-44 +4x = 64 - 44.

4x =20

Dividing both sides by 4, we get

x= 5.

Let us plug x=5 to find the length of each side, we get

AB = 44 + 3x = 44 +3(5) = 44 + 15 = 59 cm

BC = 33 + x = 33 + 5 = 38 cm

CD = 64 − x = 64 - 5 = 59 cm

AD = 48 − 2x = 48 - 2(5) = 48 - 10 = 38 cm.

We can see that AB = CD = 59 cm and BC = AD = 38 cm.

Therefore, quadrilateral ABCD is a parallelogram.