Explanation:
1A
the travel paths of the plane build a right-angled triangle.
one travels north, which creates the vertical leg.
the other travels west, which creates the horizontal leg.
their distance is the Hypotenuse (the baseline opposite of the 90° angle), which we can get via Pythagoras
c² = a² + b²
c being the Hypotenuse, a and b being the legs.
how long are the legs ?
the plane going north travels at 240 km/h for 90 minutes.
the plane going west travels at 180 lm/h for 90 minutes.
90 minutes = 1.5 hours (1 hour 30 minutes).
so,
plane 1 went 240×1.5 = 360 km.
plane 2 went 180×1.5 = 270 km.
distance² = 360² + 270² = 129600 + 72900 = 202500
distance = sqrt(202500) = 450 km
2A
again Pythagoras :
130² = 80² + (2nd leg)²
16900 = 6400 + (2nd leg)²
10500 = (2nd leg)²
2nd leg = 102.4695077... m
so, the full perimeter is
130 + 80 + 102.4695077... = 312.4695077... m
312.4695077... = 100%
1% = 100%/100 = 3.124695077... m
how many % are 220 m ? well as many as how often 1% fits into 220 m :
220 / 3.124695077... = 70.40686998... %
3A
again Pythagoras :
the legs of that inner right-angled triangle are (as you correctly wrote) 40 m and 45 m.
the fence is the Hypotenuse, and we get
fence² = 40² + 45² = 1600 + 2025 = 3625
fence = 60.20797289... m ≈ 60 m
please burn that into your brain forever for any right-angled triangle situations :
a² + b² = c²
Pythagoras