Question

what is the perimeter?
15
33
32
perimeter =
submit

Explanation:

Step1: Use tangent segment theorem

For a triangle with an incircle, tangent segments from a single external point to the circle are equal. So, $WV = X$, $UT = 15$, $WS = 32$, $ST = 33$.

Step2: Find side lengths of $\triangle SUW$

• $UW = UV + UT = 15 + 15 = 30$
• $SW = WS + WV = 32 + X$, and since $ST = 33$, $SV = 33$, so $X = 32$ (because tangent segments from $W$ are equal, tangent segments from $S$ are equal: $SV = ST = 33$, so $SW = 32 + 32 = 64$? Correction: Tangent segments from $U$: $UV=UT=15$; from $S$: $ST=SV=33$; from $W$: $WV=WX=32$.
• $SU = ST + UT = 33 + 15 = 48$
• $UW = 15 + 15 = 30$
• $SW = 32 + 33 = 65$

Step3: Calculate perimeter

Add all three side lengths: $Perimeter = SU + UW + SW$
<Expression>
$Perimeter = 48 + 30 + 65$
</Expression>

Answer:

143