Question

Given : BD is a median of ABC AC = 54x - 5 DC = 12x + 20

Answer 1

it is given that

BD = median

also,

AC = 54x - 5

and

DC = 12x + 20

we know that the median of the triangle divides the length AC in equal two parts,

so,

AC = 2 x DC

put the values,

54x - 5 = 2(12x + 20)

54x - 5 = 24x + 40

54x - 24x = 40+ 5

30x = 45

x = 45/30

x = 3/2

x = 1.5

put x = 3/2 in equation AC = 54x - 5

AC = 54 x (3/2) - 5

= 27x 3 - 5

= 81 - 5

= 76

thus, the answer is

x = 3/2 = 1.5

AC = 76