A) \[A{{C}^{2}}=\,A{{D}^{2}}+3C{{D}^{2}}\]
B) \[A{{C}^{2}}=\,A{{D}^{2}}+5C{{D}^{2}}\]
C) \[A{{C}^{2}}=\,A{{D}^{2}}+7C{{D}^{2}}\]
D) \[A{{C}^{2}}=\,A{{B}^{2}}+5B{{D}^{2}}\]
Correct Answer: B
Solution :
From right angled \[\Delta \,\,ABC,\] \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] ??.(i) Also, from right angled \[\Delta \,ABD,\] \[A{{D}^{2}}=A{{B}^{2}}+B{{D}^{2}}\] or \[A{{B}^{2}}=A{{D}^{2}}-B{{D}^{2}}\] Substituting the value in (i), we get \[A{{C}^{2}}=(A{{D}^{2}}-B{{D}^{2}})+B{{C}^{2}}\] \[=A{{D}^{2}}+(B{{C}^{2}}-B{{D}^{2}})\] \[=A{{D}^{2}}+(BC-BD)\,(BC+BD)\] or \[A{{C}^{2}}=A{{D}^{2}}+CD(3\,CD+2\,CD)\] or \[A{{C}^{2}}=A{{D}^{2}}+5\,C{{D}^{2}}\]You need to login to perform this action.
You will be redirected in
3 sec