Question

Two numbers are in the ratio 5:6. If the sum of their squares is 3904. The larger number is​

Answer 1

Two numbers are in the ratio of 5:6.

The sum of their squares is 3904

We have to find the larger number here.

If the numbers are in a ratio of 5:6, let's denotes them as 5k and 6k respectively.

Their sum of squares can be depicted as

>> (5k)² + (6k)²

>> 25k² + 36k²

>> 61k²

This is equal to 3904

So

61k² = 3904

k² = 64

k = ±8

K can have both positive as well as negative values here

If k is +ve, the numbers are 40 and 48. The larger number is 48

If k is -ve, the numbers are -40 and -48. The larger number is -40

Answer : The larger number is 48 or -40.

Answer 2

Answer -

Given -

Two numbers are in the ratio 5:6. If the sum of their squares is 3904. The larger number is

Ratio = 5:6

Let the numbers be 5x and 6x.

Their square = 3904

∴

$({5x})^{2} + ({6x})^{2} \\ = {25x}^{2} + {36x}^{2} \\ = {61x}^{2}$

This value is equal to 3904 (given)

A/C

${61x}^{2} = 3904 \\ = {x}^{2} = 3904 \div 61 \\ = {x}^{2} = 64 \\ = x = \sqrt{64} \\ = x = 8$

The numbers are 5x = 5 × 8 = 40

6x = 6 × 8 = 48

Hence, the larger number is 48.