The problem is to find the length of SU. We are given that QR = 24 ft, UV = 26 ft, and US = 36 ft. The circle with center P is tangent to the sides of triangle QUS at points R, V, and T respectively.

1. Problem Description

The problem is to find the length of SU. We are given that QR = 24 ft, UV = 26 ft, and US = 36 ft. The circle with center P is tangent to the sides of triangle QUS at points R, V, and T respectively.

2. Solution Steps

Since the circle is tangent to the sides of the triangle, we know that $QR = QV$, $US = UT$, and $VU = UR$.

Let $QR = QV = x$, $US = UT = y$, and $VU = UR = z$.

We are given $QR = 24$, $UV = 26$, and $US = 36$. So $x = 24$ ft, $US = y = 36$ ft, and $UV = z = 26$ ft.

We want to find $SU$. We know that $SU = UT + TS = y$.

Since $US = 36$ ft, then $UT = 36$ ft. This value is labeled on the figure. Thus, $SU = 36$ ft.

$US = 36$ ft.

3. Final Answer

36 ft