Question

what values of w and x make δstu ≅ δfge?
t
2w+8
2w+x+8
u
s
w =

x =

submit
f
w−5x+48
e
5w−40
g

Explanation:

Step1: Identify congruent sides

Since \( \triangle STU \cong \triangle FGE \), their corresponding sides are equal. The legs of the right triangles: \( 2w + 8 \) (from \( \triangle STU \)) and \( 5w - 40 \) (from \( \triangle FGE \)) should be equal. So, set up the equation:
\( 2w + 8 = 5w - 40 \)

Step2: Solve for \( w \)

Subtract \( 2w \) from both sides:
\( 8 = 3w - 40 \)
Add 40 to both sides:
\( 48 = 3w \)
Divide by 3:
\( w = 16 \)

Step3: Use \( w \) to find \( x \)

Now, the hypotenuses: \( 2w + x + 8 \) (from \( \triangle STU \)) and \( w - 5x + 48 \) (from \( \triangle FGE \)) are equal. Substitute \( w = 16 \):
Left hypotenuse: \( 2(16) + x + 8 = 32 + x + 8 = x + 40 \)
Right hypotenuse: \( 16 - 5x + 48 = 64 - 5x \)
Set equal: \( x + 40 = 64 - 5x \)

Step4: Solve for \( x \)

Add \( 5x \) to both sides:
\( 6x + 40 = 64 \)
Subtract 40:
\( 6x = 24 \)
Divide by 6:
\( x = 4 \)

Answer:

\( w = 16 \), \( x = 4 \)