Question

Find x. there is a picture of a triangle and I'll upload so you can see the measurements.

Answer 1

x = 3

Step-by-step explanation

Given:

Desired Outcome:

The value of x

Determine the value of 'y' from triangle BCD using Pythagorean Theorem

`\begin{gathered} Hyp^2\text{ = Opp}^2\text{ + Adj}^2 \\ CD^2\text{ = BD}^2\text{ + BC}^2 \\ 25^2\text{ = }y^2\text{ + 24}^2 \\ y^2\text{ = 625 - 576} \\ y\text{ = }√(49) \\ y\text{ = 7} \end{gathered}`

Determine the value of 'z' from triangle ABC using Pythagorean Theorem

`\begin{gathered} AC^2\text{ = AB}^2\text{ + BC}^2 \\ 26^2\text{ = z}^2\text{ + 24}^2 \\ z^2\text{ = 676 - 576} \\ z\text{ = }√(100) \\ z\text{ = 10} \end{gathered}`

Determine the value of 'x'

`\begin{gathered} AB\text{ = AD + BD} \\ z\text{ = x + y} \\ x\text{ = z - y} \\ x\text{ = 10 - 7} \\ x\text{ = 3} \end{gathered}`

Hence, the value of x is 3.