Option C – BD=76 cm
Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.
To find : How long BD should it be?
First we draw a rough diagram.
The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.
According to properties of kite
Two disjoint pairs of consecutive sides are congruent.
So, AD=AB=44.8 cm
The diagonals are perpendicular.
So, AC ⊥ BD
Let O be the point where diagonal intersect let let the partition be x and y.
Perpendicular bisect the diagonal BD into equal parts let it be z.
Applying Pythagorean theorem in ΔAOD
where H=AD=44.8 ,P= AO=x , B=OD=z
Applying Pythagorean theorem in ΔCOD
where H=DC=72 ,P= OC=y , B=OD=z
Subtract  and 
Add equation  and , to get values of x and y
Substitute x in 
Substitute value of x in equation , to get z
We know, BD=z+z
Nearest to whole number BD=76 cm
Therefore, Option c – BD=76 cm is correct.