Answer:
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
