Given: AR ⊥ RS, TS ⊥ RS, AT=26, RS=24, AR=12

Find: TS

Solution -

drawing a perpendicular from AQ to TS, we get a right angle triangle AQT

Using Pythagoras Theorem,

AT² = AQ² + QT²

⇒26² = 24² + QT² (∵ Due to symmetry AQ = RS)

⇒QT² = 676-576 = 100

⇒QT = 10

As TS = QT + QS = 12 + 10 = 22 (∵ Due to symmetry AR = QS)

∴ TS = 22 (ans)