BD = 56
Step-by-step explanation:
Step 1: In rectangle, the diagonals are congruent and bisect each other.
So, AC = BD
⇒AG + GC = BG + GD
⇒AG + AG = GD + GD
⇒ 2AG = 2GD
⇒AG = GD
⇒ –7j + 7 = 5j + 43
⇒–7j – 5j = 43 – 7
⇒–12j = 36
⇒j = –3
Step 2: BD = 2DG
BD = 2(5j + 43)
= 2(5 (–3) + 43)
= 2(–15 + 43)
= 2 × 28
= 56
Hence, BD = 56.
