Respuesta :
Correct me if I'm wrong, but i believe the correct answer should be answer C) 76 cm.
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= [tex]x+y=84.8[/tex] .......[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
[tex]H^2=P^2+B^2[/tex]
[tex](44.8)^2=x^2+z^2[/tex] .........[2]
Applying Pythagorean theorem in ΔCOD
where H=DC=72 ,P= OC=y , B=OD=z
[tex]H^2=P^2+B^2[/tex]
[tex](72)^2=y^2+z^2[/tex] ............[3]
Subtract [2] and [3]
[tex](72)^2-(44.8)^2=y^2+z^2-x^2-z^2[/tex]
[tex]5184-2007.04=(x+y)(x-y)[/tex]
[tex]3176.96=(84.8)(x-y)[/tex]
[tex]37.464=x-y[/tex] ..........[4]
Add equation [1] and [4], to get values of x and y
[tex]x+y+x-y=84.8+37.464[/tex]
[tex]2x=122.264[/tex]
[tex]x=61.132[/tex]
Substitute x in [1]
[tex]x+y=84.8[/tex]
[tex]61.132+y=84.8[/tex]
[tex]y=23.668[/tex]
Substitute value of x in equation [2], to get z
[tex](44.8)^2=x^2+z^2[/tex]
[tex](44.8)^2=(23.668)^2+z^2[/tex]
[tex]2007.04-560.174224=z^2[/tex]
[tex]z=\sqrt{1446.865776}[/tex]
[tex]z=38.06[/tex]
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.
