Answer:
[tex]\Large \boxed{\mathrm{square: 15 \ meters}} \\\\ \Large \boxed{\mathrm{triangle: 20 \ meters}}[/tex]
Step-by-step explanation:
The perimeter of a square is [tex]\sf P=4s[/tex], where s is the side length.
The perimeter of an equilateral triangle is [tex]\sf P=3a[/tex], where a is the side length.
The side length of the equilateral triangle is 5 more than the side length of the square.
[tex]\sf a = s+5[/tex]
The perimeter of the square and equilateral triangle are equal.
[tex]\sf 4s=3(s+5)[/tex]
Expanding brackets.
[tex]\sf 4s=3s+15[/tex]
Subtracting 3s from both sides.
[tex]\sf s=15[/tex]
The side length of the square is 15 meters.
[tex]\sf a=15+5 \\\\\\ a=20[/tex]
The side length of the triangle is 20 meters.
