Question

the ratio of three number is 4 : 3 : 7 and sum of their square is 666. what is the value of the largest of the three numbers?​

Answer 1

Given: the ratio of three numbers is 4 : 3 : 7 and their sum is 666

To find: the value of the largest of the three numbers

Solution:

• Let the three numbers be a, b and c.

• Then, a : b : c = 4 : 3 : 7

• Let, a = 4k, b = 3k and c = 7k, where k is constant

• Then, k = c/7

• Also, b = 3c/7 and a = 4c/7

Given that, the sum of the squares of the numbers is 666. Then

• a² + b² + c² = 666
• or, (4c/7)² + (3c/7)² + c² = 666
• or, 16c²/49 + 9c²/49 + c² = 666
• or, (16/49 + 9/49 + 1) * c² = 666
• or, (16 + 9 + 49)/49 * c² = 666
• or, 74/49 * c² = 666
• or, c² = 441
• or, c = 21

• Then, b = 9 and a = 12.

Answer: the largest number is 21.

Answer 2

Given: The ratio of three number is 4 : 3 : 7 and sum of their square is 666.

To find: What is the value of the largest of the three numbers?​

Solution:

• Let the common ratio be x, then:

• The numbers are 4x, 3x, 7x.

• Now we have given sum of their square is 666, so:

            (4x)² + (3x)² + (7x)² = 666

             16x² + 9x² + 49x² = 666

             74x² = 666

             x² = 666/74

             x² = 9

             x = 3

• Numbers :

             4(3) = 12 , 3(3) = 9 , 7(3) = 21

Answer:

            So the largest number is 21.