Final answer:
To find the length of side y in similar triangles with known sides, we use the property of similar triangles that states corresponding sides are proportional. By setting up a proportion with the given measures and solving for y, we find that the length of side y is 83.33 meters.
Step-by-step explanation:
To find the length of side y in similar triangles a and b, we can use the properties of similar triangles which state that corresponding sides are proportional. Given that x is 100 meters, n is 30 meters, and m is 25 meters, we can set up a proportion:
\(\frac{{n}}{{x}} = \frac{{m}}{{y}}\)
By plugging in the values we have:
\(\frac{{30}}{{100}} = \frac{{25}}{{y}}\)
We can solve for y by cross-multiplying:
\(30 \cdot y = 100 \cdot 25\)
\(y = \frac{{100 \cdot 25}}{{30}}\)
\(y = \frac{{2500}}{{30}}\)
\(y = 83.33\) meters
Therefore, the length of side y is 83.33 meters.