Answer:
DC = 1.92 inches
AD = 11.08 inches
Step-by-step explanation:
From the figure given above, angle ABC is a right angle triangle where
AB = 12 inches
BC = 5 inches
Use pythagorean theorem to find AC
AC^2 = AB^2 + BC^2
Substitutes all the parameters into the formula
AC^2 = 12^2 + 5^2
AC^2 = 144 + 25
AC = sqrt ( 169 )
AC = 13 in
Also,
BD^2 = AB^2 - AD^2
Let AD = 13 - x
Substitute all into the formula
BD^ = 12^2 - (13 - x)^2 ..... (1)
Moreso,
BD^2 = BC^2 - DC^2
Let DC = x
Substitute all into the formula
BD^2 = 5^2 - x^2 ...... (2)
Equate equation 1 and 2
12^2 - ( 13 - x )^2 = 5^2 - x^2
144 - (169 - 26x + x^2) = 25 - x^2
Open the bracket
144 - 169 + 26x - x^2 = 25 - x^2
-25 + 26x = 25
Collect the like terms
26x = 50
X = 50/26
X = 1.92 inches
Therefore, DC = 1.92 inches
And AD = 13 - 1.92 = 11.08 inches
