Step-by-step explanation:
if I understand you correctly the sides are in a
5 : 12 : 17 : 25 ratio.
a ratio is basically a fraction. but instead of the denominator telling us the structure of the whole (e.g. 2/5 tells us that the whole is split into 5 equal parts), a ratio tells us this by the sum of its elements :
5 : 12 : 17 : 25
means that the whole perimeter of the quadrilateral has
5 + 12 + 17 + 25 = 59 equal parts.
since the perimeter is 590 m, we know with 59 equal parts, that one part is 590/59 = 10 m.
so, the sides are
50 m, 120 m, 170 m, 250 m
but for the area of the quadrilateral there is at least the information of one angle missing.
to have just the 4 side lengths is not enough. these sides can still have all kinds of angles between them, which creates different areas.
