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.
So, 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
![H^2=P^2+B^2](https://tex.z-dn.net/?f=H%5E2%3DP%5E2%2BB%5E2)
.........[2]
Applying Pythagorean theorem in ΔCOD
where H=DC=72 ,P= OC=y , B=OD=z
![H^2=P^2+B^2](https://tex.z-dn.net/?f=H%5E2%3DP%5E2%2BB%5E2)
............[3]
Subtract [2] and [3]
..........[4]
Add equation [1] and [4], to get values of x and y
![x+y+x-y=84.8+37.464](https://tex.z-dn.net/?f=x%2By%2Bx-y%3D84.8%2B37.464)
![2x=122.264](https://tex.z-dn.net/?f=2x%3D122.264)
![x=61.132](https://tex.z-dn.net/?f=x%3D61.132)
Substitute x in [1]
![x+y=84.8](https://tex.z-dn.net/?f=x%2By%3D84.8)
![61.132+y=84.8](https://tex.z-dn.net/?f=61.132%2By%3D84.8)
![y=23.668](https://tex.z-dn.net/?f=y%3D23.668)
Substitute value of x in equation [2], to get z
![(44.8)^2=x^2+z^2](https://tex.z-dn.net/?f=%2844.8%29%5E2%3Dx%5E2%2Bz%5E2)
![(44.8)^2=(23.668)^2+z^2](https://tex.z-dn.net/?f=%2844.8%29%5E2%3D%2823.668%29%5E2%2Bz%5E2)
![2007.04-560.174224=z^2](https://tex.z-dn.net/?f=2007.04-560.174224%3Dz%5E2)
![z=\sqrt{1446.865776}](https://tex.z-dn.net/?f=z%3D%5Csqrt%7B1446.865776%7D)
![z=38.06](https://tex.z-dn.net/?f=z%3D38.06)
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.