The ratio of three numbers is 3:4:5 and the sum of their squares is 1250. The sum of the three numbers is:
30
90
60
50
A
50
B
90
C
60
D
30
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Solution
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Let the three numbers be 3x,4x and 5x. Given (3x)2+(4x)2+(5x)2=1250 9x2+16x2+25x2=1250 ⇒50x2=1250⇒x2=25⇒x=5 ∴ The three numbers are 3×5,4×5 and 5×5 i.e., 15,20 and 25 Required sum =15+20+25=60
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