Question

can u please give me the answer​

Answer 1

Since the sides are in the ratio a : b where a and b are assumed as positive and coprime integers, let the sides of the two squares be ax and bx.

Then their areas will be a²x² and b²x². Given that these are in the ratio 25 : 9. So,

a²x² / b²x² = 25 / 9

a² / b² = 5² / 3²

Thus we get,

a / b = 5 / 3

Since a and b are coprime integers, then one can make the following equations true.

a = 5 ; b = 3

Then their sum is,

a + b = 5 + 3

a + b = 8

But if the two integers a and b are not strictly coprimes, let,

a = 5k ; b = 3k

Then their sum will be,

a + b = 5k + 3k

a + b = 8k

Hence their sum can be any integral multiple of 8.

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