P Q R S is a quadrilateral and P Q = a , Q R = b , S P = a - b , M is the mid-point of Q R and X is a point on S M such that S X = 4 5 S M . If S M =m(4 a - b ) and S X =n(4 a - b ) , then m+n=

Step-by-step solution

aligned & S Q=S P+P Q=(a-b)+a=2 a-b & S M=S Q+Q M=(2 a-b)+ b 2 =2 a- b 2 aligned S M = 1 2 (4 a - b ) m= 1 2 S X = 4 5 S M (given) = 4 5 1 2 (4 a-b) S X= 2 5 (4 a-b) n= 2 5 Hence, m+n= 1 2 + 2 5 = 9 10