Question

There are three positive numbers in the ratio 6:7:8
If the sum of the squares of the smallest
largest numbers is 1600, find the number
(A) 6, 7, 8
(B) 12, 14, 16
(C) 18, 21, 24
(D) 24, 28, 32​

Answer 1

Answer:

(D) 24,28,32 is the answer

Step-by-step explanation:

As the three positive numbers are in the ratio 6:7:8, we can assign them as:

6x, 7x and 8x

Given: sum of squares of smallest and largest is 1600

=> (6x)² + (8x)² = 1600

=> 36x² + 64x² = 1600

=> 100x² = 1600

=> x² = 16

=> x = 4

(Please note that as the numbers are positive, x = -4 is inadmissible.)

As the given numbers are: 6x, 7x, 8x, the numbers will be:

6*4, 7*4, 8*4

= 24, 28, 32