*In right triangled ABC right angled at B ,a line DE is drawn through the mid point D of AB and parallel to BC.If AB=9 cm, BC=12 cm. AE=?* Give explanation.
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SolutioN :-
As DE ║ BC
★ ΔADE ≈ ΔABC
→ AD/AB = AE / AC
→ AD /DB = 1/2
→ DB/AD = 2
Adding 1 both sides
→ DB/AD + 1 = 2 + 1
→ (DB + AD)/AD =3
→ DB + AD = AB
→ AB/AD = 3
→ AD/AB = 1/3
→ AE / AC = 1/3
→ AE = AC/3
★ AC² = AB² + BC²
→ AC² = 9² + 12²
→ AC² = 81 + 144
→ AC² = 225
→ AC = √225
→ AC = 15
★ AE = AC/3
→ AE = 15/3
→ AE = 5 cm
∴ Length of AE is 5 cm
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