Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers are in the ratio of 3: 4, find the numbers.

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Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers are in the ratio of 3: 4, find the numbers.

A8, 18

B9, 12

C9, 13

D6, 8

Answer:

D. 6, 8

Read Explanation:

The two numbers are in the ratio = 3x : 4 x

According to the question $(4x) ^ 2 + 224 = 8 \times (3x) ^ 2$

$\Rightarrow 16x ^ 2 + 224 = 8 \times 9x ^ 2$

$\Rightarrow x = 2$

The number are 3 x 2 = 6 and 4 x 2 = 8

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