Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 242: 41

TS = 13 RT = 18.38

Since RSTV and WXYZ are squares, all the sides are equal, and thus ZT=SY=RX=WV=5 Since STY is a right-angled triangle, by using the Pythagorean Theorem, $TS^{2}= 5^{2}+12^{2}=169$ $TS=13$ Since RST is a right-angled triangle, by using the Pythagorean Theorem, $RT^{2}=13^{2}+13^{2}=338$ $RT=\sqrt 338=18.384776...$ $RT\approx18.38$