Three positive integers are in the ratio 1 3 5.If the sum of their squares is 315,find the largest number

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Solution

Dear Student,

Let the positive integers be $x, 3 x, 5 x$ . Then
$x^{2} + {(3 x)}^{2} + {(5 x)}^{2} = 315 \Rightarrow x^{2} + 9 x^{2} + 25 x^{2} = 315 \Rightarrow 35 x^{2} = 315 \Rightarrow x^{2} = \frac{315}{35} \Rightarrow x^{2} = 9 \Rightarrow x = 3 [T h e y a r e a l l p o s i t i v e] 3 x = 3 \times 3 = 9 5 x = 5 \times 3 = 15 T h u s, t h e l a r g e s t i n t e g e r i s 15 .$
Regards,

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Three positive integers are in the ratio 1 3 5.If the sum of their squares is 315,find the largest number

Dear Student, Let the positive integers be x, 3x, 5x. Then x2+3x2+5x2=315⇒x2+9x2+25x2=315⇒35x2=315⇒x2=31535⇒x2=9⇒x=3 They are all positive3x=3×3=95x=5×3=15Thus, the largest integer is 15. Regards,