Answer:
Case 1: 50.35 cm
Case 2: 56.715 cm
Step-by-step explanation:
AB = AC;
½ X AH x BC = 100 cm2
=> AH x BH = 100 cm2
=> AH = 100/BH
Case 1: (BAC)= [tex]\pi[/tex]/6
S = ½ x AB x AC x sin (BAC) = 100 cm2
AB^2 x sin [tex]\pi[/tex]/6 = 200
=> AB^2 x ½ = 200
=> AB = 20 cm = AC
BC^2 = AB^2 + AC^2 – 2 x AB x AC x cos (BAC) = 202 + 202 – 2 x 20 x 20 x [tex]\sqrt{3}[/tex]/2 = (800 - 400[tex]\sqrt{3}[/tex]) cm
=> BC = 10.35 cm
Perimeter: AB + AC + BC = 20 + 20 + 10.35 = 50.35 cm
Case 2: (ABC) = [tex]\pi[/tex]/6 => (BAC) = 2[tex]\pi[/tex]/3
S = ½ x AB x AC x sin (BAC) = 100 cm2
AB^2 x sin 2[tex]\pi[/tex]/3 = 200
=> AB^2 x [tex]\sqrt{3}[/tex]/2 = 200
=> AB^2 = 400/[tex]\sqrt{3}[/tex]
=> AB = AC = 15.197 cm
BC^2 = AB^2 + AC^2 – 2 x AB x AC x cos (BAC) = 400/[tex]\sqrt{3}[/tex] + 400/[tex]\sqrt{3}[/tex] – 2 x 400/[tex]\sqrt{3}[/tex] x (-1/2) = 692.82 cm
=> BC = 26.321
Perimeter: AB + AC + BC = 15.197 + 15.197 + 26.321 = 56.715 cm
