**Answer:**

Option C – BD=76 cm

**Step-by-step explanation:**

**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?

**Solution : **

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

DC=BC=72 cm

**The diagonals are perpendicular.**

**S**o, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC= …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

**Applying Pythagorean theorem in ΔAOD**

where H=AD=44.8 ,P= AO=x , B=OD=z

………[2]

**Applying Pythagorean theorem in ΔCOD**

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

**Subtract [2] and [3]**

……….[4]

**Add equation [1] and [4], to get values of x and y**

**Substitute x in [1]**

**Substitute value of x in equation [2], to get z**

**We know, **BD=z+z

BD= 38.06+38.06

BD= 76.12

**Nearest to whole number **BD=76 cm

**Therefore, Option c – BD=76 cm is correct.**