Question

You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm. You want to use a straight crossbar BD About how long should it be?

Round your answers to the nearest whole number. The diagram is not drawn to scale.

a.
BD = 85 cm
c.
BD = 76 cm
b.
BD = 3,799 cm
d.
BD = 2,007 cm

Answer 1

Correct me if I'm wrong, but i believe the correct answer should be answer C) 76 cm. 

Answer 2

Option C - BD=76 cm

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=
`x+y=84.8` .......[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`

`(44.8)^2=x^2+z^2` .........[2]

Applying Pythagorean theorem in ΔCOD

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

`H^2=P^2+B^2`

`(72)^2=y^2+z^2` ............[3]

Subtract [2] and [3]

`(72)^2-(44.8)^2=y^2+z^2-x^2-z^2`

`5184-2007.04=(x+y)(x-y)`

`3176.96=(84.8)(x-y)`

`37.464=x-y` ..........[4]

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

`x+y+x-y=84.8+37.464`

`2x=122.264`

`x=61.132`

Substitute x in [1]

`x+y=84.8`

`61.132+y=84.8`

`y=23.668`

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

`(44.8)^2=x^2+z^2`

`(44.8)^2=(23.668)^2+z^2`

`2007.04-560.174224=z^2`

`z=√(1446.865776)`

`z=38.06`

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.