3 Sum of three numbers which are in the ratio 3:4:5 is 60. What is the sum of
their squares?
(A)1970
(B)1430
(

2 thoughts on “3 Sum of three numbers which are in the ratio 3:4:5 is 60. What is the sum of<br />their squares?<br />(A)1970<br />(B)1430<br />(”

1. Answer:

   Given :-

   • Sum of three numbers are in the ratio of 3 : 4 : 5 is 60.

   To Find :-

   • What is the sum of their squares.

   Solution :-

   Let,

   [tex]\mapsto[/tex] First number = 3x

   [tex]\mapsto[/tex] Second number = 4x

   [tex]\mapsto[/tex] Third number = 5x

   According to the question,

   [tex]\implies \sf 3x + 4x + 5x =\: 60[/tex]

   [tex]\implies \sf 7x + 5x =\: 60[/tex]

   [tex]\implies \sf 12x =\: 60[/tex]

   [tex]\implies \sf x =\: \dfrac{\cancel{60}}{\cancel{12}}[/tex]

   [tex]\implies \sf x =\: \dfrac{5}{1}[/tex]

   [tex]\implies \sf\bold{\green{x =\: 5}}[/tex]

   Hence, the required numbers are :

   [tex]\dashrightarrow[/tex] First number :

   [tex]\leadsto \sf 3x[/tex]

   [tex]\leadsto \sf 3(5)[/tex]

   [tex]\leadsto \sf 3 \times 5[/tex]

   [tex]\leadsto\sf\bold{\purple{15}}[/tex]

   [tex]\dashrightarrow[/tex] Second number :

   [tex]\leadsto \sf 4x[/tex]

   [tex]\leadsto \sf 4(5)[/tex]

   [tex]\leadsto \sf 4 \times 5[/tex]

   [tex]\leadsto \sf\bold{\purple{20}}[/tex]

   [tex]\dashrightarrow[/tex] Third number :

   [tex]\leadsto \sf 5x[/tex]

   [tex]\leadsto \sf 5(5)[/tex]

   [tex]\leadsto \sf 5 \times 5[/tex]

   [tex]\leadsto \sf\bold{\purple{25}}[/tex]

   Hence, the three numbers are 15, 20 and 25 respectively.

   Now, we have to find their squares :

   [tex]\bigstar \sf {(15)}^{2} =\: 15 \times 15 =\: \bold{\purple{225}}\\[/tex]

   [tex]\bigstar \sf {(20)}^{2} =\: 20 \times 20 =\: \bold{\purple{400}}\\[/tex]

   [tex]\bigstar \sf {(25)}^{2} =\: 25 \times 25 =\: \bold{\purple{625}}\\[/tex]

   Hence, their squares are 225, 400 and 625 respectively.

   Now, we have to find the sum of their squares :

   [tex]\Rightarrow \sf Sum\: of\: their\: squares =\: 225 + 400 + 625\\[/tex]

   [tex]\Rightarrow \sf Sum\: of\: their\: squares=\: 625 + 625\\[/tex]

   [tex]\Rightarrow \sf\bold{\red{Sum\: of\: their\: squares =\: 1250}}\\[/tex]

   [tex]\therefore[/tex] The sum of their squares is 1250 .

   Hence, the correct options is option no (c) 1250 .

   [tex]\rule{150}{2}[/tex]

   VERIFICATION :

   [tex]\implies \sf 3x + 4x + 5x =\: 60[/tex]

   By putting x = 5 we get,

   [tex]\implies \sf 3(5) + 4(5) + 5(5) =\: 60[/tex]

   [tex]\implies \sf 15 + 20 + 25 =\: 60[/tex]

   [tex]\implies \sf\bold{60 =\: 60}[/tex]

   Hence, Verified.

   Reply

2. Let the three numbers of 3x, 4x, and 5x, Sum of the squares of these = 1250.

   A/q,

   [tex] = (3x) {}^{2} + (4x) {}^{2} + (5x) {}^{2} = 1250 [/tex]

   [tex] = > 9x { }^{2} +16x {}^{2} + 25x {}^{2} = 1250 [/tex]

   [tex] = > 50x {}^{2} = 1250 [/tex]

   [tex] = >x {}^{2} = 1250 \div 50 [/tex]

   [tex] = >x {}^{2} = 25 [/tex]

   [tex] = > x = 5[/tex]

   Therefore, three numbers are:-

   [tex] = > 3x = 3(5) = 15[/tex]

   [tex] = > 4x = 4(5) = 20[/tex]

   [tex] = > 5x = 5(5) = 25[/tex]

   Now,

   Sum of these number = 15 + 20 + 25 = 60

   Required Answer = 60.

   Step-by-step explanation:

   @Genius

   Reply