Question

what is rw?
22
15
15
$rw = \square$
submit

Explanation:

Step1: Define tangent segment variables

Let $RW = x$, $WT = WV = y$, $UT = US = z$.

Step2: Set up perimeter equations

For $\triangle USW$: $US + SW + WU = 2z + 2y$
$SW = SR + RW = 15 + x$, $WU = WV + VU = y + z$, $US = z$
So $z + (15 + x) + (y + z) = 2(z + y)$
Simplify: $2z + y + 15 + x = 2z + 2y$ → $x + 15 = y$
For segment $SU$: $SU = ST + TU$, $SU = 22 - z$, $TU = z$ → $22 - z = z$ → $z = 11$
For side $SW$: $SW = 15 + x$, and $SW = SR + RW = 15 + x$, also $WU = 15 = y + z$

Step3: Solve for y and x

Substitute $z=11$ into $15 = y + 11$: $y = 15 - 11 = 4$
Use $x + 15 = y$ → $x = y - 15$? Correct: Use perimeter of $\triangle USW$:
Perimeter = $22 + 15 + 15 = 52$, semi-perimeter $s = 26$
$SU = 22 = s - RW$ → $22 = 26 - x$

Step4: Calculate final value

$x = 26 - 22 = 4$

Answer:

4