Respuesta :

Hrishii

Answer:

x = 4.5

[tex]P(\triangle PQR) = 52\: units[/tex]

Step-by-step explanation:

  • Lengths of tangents drawn from an external point to a circle are equal.

  • -> PS = PT

  • -> PS = 9 units (PT = 9 units)

  • - > 2x = 9

  • -> x = 9/2

  • -> x = 4.5

  • Using the same property of tangents, we find:

  • QU = QT = 4 units

  • RU = RS = 13 units

  • PQ = PT + QT = 9 + 4 = 13 units

  • QR = QU + RU = 4 + 13 = 17 units

  • PR = PS + RS = 9 + 13 = 22 units

  • [tex]P(\triangle PQR) = PQ + QR + PR[/tex]

  • [tex]\implies P(\triangle PQR) = 13 + 17 + 22[/tex]

  • [tex]\implies \huge\orange{P(\triangle PQR) = 52\: units}[/tex]

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