Question

B is the midpoint of AC. AB=x^ 2 . BC=4x+5 Find AC

Answer 1

AC = 50

Explanation:

Since, B is the midpoint of AC.

`\therefore AB = BC\\</p><p>\therefore x^2 = 4x + 5\\</p><p>\therefore x^2 - 4x - 5 =0\\</p><p>\therefore x^2 - 5x + x - 5= 0\\</p><p>\therefore x(x - 5) +1(x - 5)=0\\</p><p>\therefore (x - 5)(x + 1) =0\\</p><p>\therefore x - 5 = 0\: or \: x + 1 = 0\\</p><p>\therefore x = 5 \: or \: x = - 1\\ \because x = - 1 \: doesn't \: satisfy\: the\: \\condition \: of \: midpoint \\ </p><p>\therefore x =5\\</p><p></p><p>\because AC = AB + BC\\</p><p>\therefore AC = x^2 + 4x + 5\\</p><p>\therefore AC = x^2 + 4x + 5 \\</p><p>\therefore AC = 5^2 + 4* 5 + 5\\</p><p>\therefore AC = 25 + 20 +5\\</p><p>\huge \red {\boxed {\therefore AC = 50}}`