Question

what values of s and t make $\triangle uvw \cong \triangle fge$?
(image of two right triangles: $\triangle uvw$ with right angle at w, leg $2t + 16$, hypotenuse $11s$; $\triangle fge$ with right angle at e, leg $4t$, hypotenuse $18s - 49$)
$s = \square$
$t = \square$

Explanation:

Step1: Solve for \( s \)

Since \( \triangle UVW \cong \triangle FGE \), their corresponding sides are equal. The hypotenuses \( UV \) and \( FG \) should be equal, so \( 11s = 18s - 49 \).
Subtract \( 11s \) from both sides: \( 0 = 7s - 49 \).
Add 49 to both sides: \( 49 = 7s \).
Divide by 7: \( s = 7 \).

Step2: Solve for \( t \)

The legs \( UW \) and \( FE \) should be equal (since the triangles are right - angled and congruent). So \( 2t + 16 = 4t \).
Subtract \( 2t \) from both sides: \( 16 = 2t \).
Divide by 2: \( t = 8 \).

Answer:

\( s = 7 \), \( t = 8 \)