Question

What the values of y and z make def = Sqr

Answer 1

The Hypotenuse-Leg Theorem states that two right triangles are congruent if and only if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of the other right triangle.

Using this theorem in our problem, we get the following two equations

$\begin{gathered} 8z=16z-24 \\ 12y-32=8y \end{gathered}$

Solving the first equation we have

$\begin{gathered} 8z=16z-24 \\ 8z-16z=16z-24-16z \\ -8z=-24 \\ 8z=24 \\ z=\frac{24}{8} \\ z=3 \end{gathered}$

The value for z is 3.

Solving the second equation, we have

$\begin{gathered} 12y-32=8y \\ 12y-32+32-8y=8y+32-8y \\ 4y=32 \\ y=\frac{32}{4} \\ y=8 \end{gathered}$

The value for y is 8.