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?

Geometry

The perimeter of kite is 172.11 cm

Step-by-step 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 = ×   ×

Area of ΔBCD = × ×

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

1800 = × +   × = ×

⇒

⇒ h = 20

AB = cm

BC = 50 cm

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

⇒

⇒100 + 20

⇒172.11 cm

Hence the perimeter of kite is 172.11 cm

d

step-by-step explanation: