Question

Three numbers are in the ratio 4:5:6. If the sum of their squares is 308, find the smallest of the three numbers.

Answer 1

Answer:

Given that the three numbers are in the ratio 4:5:6.

Let the three numbers be 4x,5x and 6x respectively.

Now,

According to the question-

6x+4x=5x+55

10x−5x=55

⇒x=

5

55

=11

Therefore,

First no. =4×11=44

Second no. =5×11=55

Third no. =6×11=66

Hence the three numbers are 44,55 and 66.

Answer 2

$({4x})^{2} + ( {5x}) ^{2} + ( {6x})^{2} = 308$

$16 {x}^{2} + 25 {x}^{2} + 36 {x}^{2} = 308$

$77 {x}^{2} = 308$

${x}^{2} = \frac{308}{77}$

${x}^{2} = 4$

$x = \sqrt{4}$

$x = 2$

smallest number is 2×4=8

largest number is 2×6=12