Question

Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure m^2-n^2 and 2mn

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Answer 1

√m^4 + n^4 +2m²n²

Explanation:

Given the following

Opposite= m²-n²

adjacent = 2mn

Using pythagoras theorem

hyp² = (m²-n²)²+(2mn)²

hyp² = m^4-2m²n²+n^4+4m²n²

hyp² = m^4 + n^4 +2m²n²

hyp = √m^4 + n^4 +2m²n²

hence the required expression is √m^4 + n^4 +2m²n²