Question

What is RT? Please help show steps!!

Answer 1

Hello from MrBillDoesMath!

Answer:

RT = sqrt(110)

Discussion:

The geometric situation shown arises when one is proving the Pythagorean theorem using similar triangles. A key result, because of triangle similarity, is that

QT/RT = RT/TS => cross multiply

RT^2 = QT * TS => substitute our numbers

RT^2 = 5 * 22

RT^2 = 110

RT = sqrt(110)

Thank you,

MrB

Answer 2

`√(110)=10.488`

Explanation:

∵ΔQRS is a right angled triangle

∵ RT ⊥ QS

∴
`RT^(2)` = QT × TS Theorem

∴
`RT^(2)` = 5 × 22 = 110

∴ RT =
`√(110)=10.488`

Theorem:

`RQ^(2)=(QT)(QS)\\ RS^(2)=(ST)(SQ)\\ RT^(2) =(QT)(TS)\\(RQ)(RS)=(QT)(TS)`