Question

Find the value of x and y.answers x = 192y = 48x = 96y = 24x = 13.9y = 6.9x = 6.9y = 6.9

Answer 1

Write the pythagorean theorem for each one of the 3 right traingles:

`\begin{gathered} 16^2=z^2+x^2 \\ \\ z^2=y^2+4^2 \\ \\ x^2=y^2+12^2 \end{gathered}`

1. Solve x^2 in the first equation:

`x^2=16^2-z^2`

2. Solve y^2 in the second equation:

`y^2=z^2-4^2`

3. Substitute the x^2 and y^2 in the third equation by the values you get in the previous steps:

`16^2-z^2=z^2-4^2+12^2`

4. Solve z^2:

`\begin{gathered} -z^2-z^2=-4^2+12^2-16^2 \\ -2z^2=-16+144-256 \\ -2z^2=-128 \\ z^2=(-128)/(-2) \\ \\ z^2=64 \end{gathered}`

5. Use the value of z^2 to solve x and y:

`\begin{gathered} x^2=16^2-z^2 \\ x^2=256-64 \\ x^2=192 \\ x=√(192) \\ x\approx13.9 \\ \\ \\ y^2=z^2-4^2 \\ y^2=64-16 \\ y^2=48 \\ y=√(48) \\ y\approx6.9 \end{gathered}`Then, the values of x and y are:x=13.9y=6.9