The figure shows a right-angled triangle and a semicircle. PQ is the diameter of the semicircle. Find the perimeter of the whole figure. (a) 13 + 8 py (b) 30 + 5py (c) 18 + 6py (d) 18 + 10py
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Using Pythagoras theorem in the right triangle, we get
PQ²=(13²-5²) cm²
⇒PQ²=144 cm²
⇒PQ=12 cm
Thus, diameter of the semi-circle = 12 cm
⇒Radius of the semi-circle = 6 cm.
Circumference of the semi-circle =½(2πr) = 6π cm
Thus, perimeter of the figure = (13 + 5 + 6π)cm = (18 + 6π)cm
The correct answer is option (C).
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