Question

Amanda wants to fly a kite. The kite is composed of two isosceles triangles,

ΔABD and ΔBCD. The height of ΔBCD is 2 times the height of ΔABD, and
the width of the kite, BD, is 1.5 times the height of the larger triangle.
If the area of the kite is 1800 cm²
, what is the perimeter of the kite?

Answer 1

idk

Explanation:

idk idk idk

Answer 2

Geometry

The perimeter of kite is 172.11 cm

Explanation:

ΔABD and ΔBCD are isosceles triangles

Join the two points A and C and the let the point be O where this lines cuts BD

Given

CO = 2 × AO ( CO is height of ΔBCD, AO is height of ΔA

BD )

and

BD = 1.5 × CO

Area of Kite = Area of ΔBCD + Area of ΔABD

If the height of ΔABD = h then height of ΔBCD =2×h

DB = 1.5 × 2×h = 3×h

Area of ΔABD =
`(1)/(2)` ×
`3h` ×
`2h`

Area of ΔBCD =
`(1)/(2)`×
`3h`×
`h`

Area of Kite = 1800 = Area of ΔABD + Area of ΔBCD

1800 =
`(6)/(2\\)` ×
`h^(2)` +
`(3)/(2)` ×
`h^(2)` =
`(9)/(2)` ×
`h^(2)`

⇒
`h^(2) = 400\\`

⇒ h = 20

`AB^(2) = (20)^(2) + (30 )^(2)`

AB =
`10√(13)` cm

`BC^(2) = 40^(2) + 30^(2)`

BC = 50 cm

So the perimeter of kite = AB + BC +CD +AD

⇒
`10√(13) + 50 + 50 + 10√(13)`

⇒100 + 20
`√(13)`

⇒172.11 cm

Hence the perimeter of kite is 172.11 cm