The perimeter of a right-angled triangle measures 234 m and the hypotenuse measures 97 m. Then the other two sides of the triangle are measured as

Hypotenuse = 97 m and perimeter = 234 m
Let the other two sides be $$a$$ m and $$b$$ m.$$
So, $$a + b = (234 - 97)$$ m = 137 m...........(i)
Also, by Pythagoras Theorem, $$a^2 + b^2 = 97^2$$
Or, $$(a + b)^2 - 2ab = 9409$$
Or, $$2ab = 137^2 - 9409$$
Or, $$2ab = 9360$$........(ii)
$$(a - b)^2 = a^2 + b^2 - 2ab$$ = $$97^2 - 9360$$ = 49
So, $$(a - b)$$ =  7 [Assuming $$a > b$$]..........(iii)
Solving (i) and (iii), we get
$$a = 72$$m and $$b = 65$$m
Hence, option B is the correct answer.