Question

AB = 44 + 3xBC = 33 + yCD = 64 − xAD = 48 − 2yQuadrilateral 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?A)51 cm , 30 cmB)55 cm , 33 cmC)59 cm , 38 cmD)64 cm , 42 cm

Answer 1

The lengths (in centimeters) of the opposite side pairs are 59 cm , 38 cm. Option C) is the correct answer.

Step-by-step explanation:

step 1 :

Given that,

Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent.

step 2 :

The opposite sides are AB and CD respectively.

The another opposite sides are BC and AD respectively.

step 3 :

If both pairs of opposite sides are congruent, then

AB = CD

44+3x = 64-x

3x+x = 64-44

4x = 20

x = 5

step 4 :

BC = AD

33+y = 48-2y

y+2y = 48-33

3y = 15

y = 5

step 5 :

Subsitute x=5 and y=5 in any of the given sides,

CD = 64-x = 64-5 = 59

∴ CD = 59 cm

BC = 33+y = 33+5 = 38

∴ BC = 38 cm

The lengths of the opposite side pairs are 59 cm , 38 cm.