Question

In 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

Explanation:

Answer 2

31 units

Explanation:

Given

`AD = 3x + 7`

`BC = 5x - 9`

Required

Find

If AD parallel to BC, then:

`AD = BC`

This gives:

`3x + 7 = 5x - 9`

Collect like terms

`3x- 5x = -7-9`

`-2x = -16`

Solve for x

`x = 8`

Substitute
`x = 8` in
`AD = 3x + 7`

`AD = 3 * 8 + 7`

`AD = 31`