Find the measures of line segments AD and DC. Show your work.

Ab = 12in
Bc=5in

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

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