If \(x:y=4:3\), then \((x^{2}+y^{2}):(x^{2}-y^{2})\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{25}{7}\)
A ratio \(x:y=4:3\) tells us only the relative size of \(x\) and \(y\), so they can be written as \(x=4k\) and \(y=3k\) for some number \(k\). Both expressions then carry \(k^{2}\), which cancels in the ratio, so the answer does not depend on \(k\).
Sum of the squares: \(x^{2}+y^{2}=16k^{2}+9k^{2}=25k^{2}\)
Difference of the squares: \(x^{2}-y^{2}=16k^{2}-9k^{2}=7k^{2}\)
Their ratio: \(\displaystyle\frac{25k^{2}}{7k^{2}}=\frac{25}{7}\)