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 = [tex]\frac{1}{2}[/tex] × [tex]3h[/tex] × [tex]2h[/tex]
Area of ΔBCD = [tex]\frac{1}{2}[/tex]× [tex]3h[/tex]× [tex]h[/tex]
Area of Kite = 1800 = Area of ΔABD + Area of ΔBCD
1800 = [tex]\frac{6}{2\\}[/tex] × [tex]h^{2}[/tex] + [tex]\frac{3}{2}[/tex] × [tex]h^{2}[/tex] = [tex]\frac{9}{2}[/tex] ×[tex]h^{2}[/tex]
⇒ [tex]h^{2} = 400\\[/tex]
⇒ h = 20
[tex]AB^{2} = (20)^{2} + (30 )^{2}[/tex]
AB = [tex]10\sqrt{13}[/tex] cm
[tex]BC^{2} = 40^{2} + 30^{2}[/tex]
BC = 50 cm
So the perimeter of kite = AB + BC +CD +AD
⇒ [tex]10\sqrt{13} + 50 + 50 + 10\sqrt{13}[/tex]
⇒100 + 20[tex]\sqrt{13}[/tex]
⇒172.11 cm
Hence the perimeter of kite is 172.11 cm
