Question

find the value of the variable rounded to the nearest tenth name the theorem used

Answer 1

The figure can be redraw as,

Consider the triangle ACD.

Determine the measure of side AC by using th pythagoras theorem.

$\begin{gathered} (AC)^2=(4)^2+(8)^2 \\ =16+64 \\ =80 \end{gathered}$

Consider the triangle ADB.

Determine the measue of side AB, in terms of variable x, by using pythagoras theorem.

$\begin{gathered} (AB)^2=(4)^2+x^2 \\ =16+x^2 \end{gathered}$

Consider the triangle ABC.

Determine the measure of side AB by using the pythagoras theorem.

$\begin{gathered} (AB)^2=(8+x)^2-(AC)^2 \\ 16+x^2=64+x^2+16x-80 \\ 16+x^2=x^2+16x-16 \\ 16x=32 \\ x=\frac{32}{16} \\ =2 \end{gathered}$

The value of variable x is 2.