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  10 +4√14

Step-by-step explanation:

PQR is a right triangle. Leg QR is shown as 5 units. Leg RP will be the sum of the radius of the circle (5) and the external measure, 4:

  RP = RT +TP = 5 + 4 = 9

Then by the Pythagorean theorem, the side PQ can be found to be ...

  PR^2 = PQ^2 +QR^2

  9^2 = PQ^2 +5^2

  PQ = √(81 -25) = √56 = 2√14

So, the sum of lengths PQ and QR is ...

  PQ +QR = 2√14 +5

The perimeter of this symmetrical figure is twice this value, so is ...

  perimeter = 2(2√14 +5)

  perimeter = 10 +4√14

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Step-by-step explanation: