Question

Quadrilateral ABCD is a rectangle.

If AG = –7y + 5 and DG = 2y + 68, find BD.


A) 108

B) -7

C) 27

D) 54

Answer 1

Answer:

A

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other, so

AC = BD

2AG = 2DG, that is

AG = DG, substitute values

- 7y + 5 = 2y + 68 ( subtract 2y from both sides )

- 9y + 5 = 68 ( subtract 5 from both sides )

-9y = 63 ( divide both sides by - 9 )

y = - 7

Hence

BD = 2(2y + 68)

     = 4y + 136

     = (4 × - 7) + 136

     = - 28 + 136

     = 108 → A