Respuesta :

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

Ashraf82

Answer:

[tex]\sqrt{110}=10.488[/tex]

Step-by-step explanation:

∵ΔQRS is a right angled triangle

∵ RT ⊥ QS

∴ [tex]RT^{2}[/tex] = QT × TS  Theorem

∴ [tex]RT^{2}[/tex] = 5 × 22 = 110

∴ RT = [tex]\sqrt{110}=10.488[/tex]

Theorem:

[tex]RQ^{2}=(QT)(QS)\\ RS^{2}=(ST)(SQ)\\ RT^{2} =(QT)(TS)\\(RQ)(RS)=(QT)(TS)[/tex]

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