Points M and N are on the sides PQ and QR respectively of a triangle PQR. right angled at Q. If PN = 9 cm, MR = 7 cm, and MN = 3 cm, then find the length of PR (in cm).

From right angled triangle QMN,

b$$^2$$ + c$$^2$$ = 3$$^2$$ 

b$$^2$$ + c$$^2$$ = 9..........(1)

From right angled triangle PQN,

(a+b)$$^2$$ + c$$^2$$ = 9$$^2$$

a$$^2$$ + b$$^2$$ + 2ab + c$$^2$$ = 81

a$$^2$$ + 2ab + 9 = 81  [From (1)]

a$$^2$$ + 2ab = 72..........(2)

From right angled triangle MQR,

b$$^2$$ + (c+d)$$^2$$ = 7$$^2$$

b$$^2$$ + c$$^2$$ + d$$^2$$ + 2cd = 49

9 + d$$^2$$ + 2cd = 49 [From (1)]

d$$^2$$ + 2cd = 40..........(3)

From right angled triangle PQR,

(a+b)$$^2$$ + (c+d)$$^2$$ = PR$$^2$$

a$$^2$$ + 2ab + b$$^2$$ + c$$^2$$ + d$$^2$$ + 2cd = PR$$^2$$

72 + 9 + 40 = PR$$^2$$

PR$$^2$$ = 121

PR = 11 cm

Hence, the correct answer is Option A