Question

n quadrilateral ABCD, AD ∥ BC. Quadrilateral A B C D is shown. Sides A D and B C are parallel. The length of A D is 3 x + 7 and the length of B C is 5 x minus 9. What must the length of segment AD be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 units

Answer 1

(c) 31 units

Explanation:

Given quadrilateral ABCD has AD║BC, with AD=3x+7 and BC=5x-9, you want to know the length of AD for the quadrilateral to be a parallelogram.

Congruent sides

Opposite sides of a parallelogram are congruent, so for ABCD to be a parallelogram, we must have ...

BC = AD

5x -9 = 3x +7

2x = 16

x = 8

AD = 3x +7 = 3(8) +7 = 31

The length of AD must be 31 units if ABCD is to be a parallelogram.

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