Question

what values of b and c make WXY congruent to FEG in

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.

From this theorem, we know that corresponding sides must be equal for those triangles to be congruent. Then, we get two equations

$\begin{gathered} c-2=2c-22 \\ 4b+18=b+48 \end{gathered}$

Let's start solving the equation for b.

$4b+18=b+48$

We can start by subtracting 18 from both sides of the equation

$\begin{gathered} 4b+18-18=b+48-18 \\ 4b=b+30 \end{gathered}$

Now, we can subtract b from both sides.

$\begin{gathered} 4b-b=b+30-b \\ (4-1)b=30 \\ 3b=30 \end{gathered}$

And finally, dividing both sides by 3 we have

$\begin{gathered} \frac{3b}{3}=\frac{30}{3} \\ b=10 \end{gathered}$

Now we have our b value. b = 10. Now, let's calculate the value for c.

$c-2=2c-22$

We can start by adding 22 to both sides of the equation

$\begin{gathered} c-2+22=2c-22+22 \\ c+20=2c \end{gathered}$

Now, we can just subtract c from both sides to get our value

$\begin{gathered} c+20-c=2c-c \\ 20=(2-1)c \\ c=20 \end{gathered}$

Then, we have our c value, c = 20.