Answer:
the triangle
Explanation:
The perimeter is the sum of the all sides of the shape.
Triangle:
3√147+2√108+2√48+3√75+ 6√12
147=49•3, 108=36•3, 48=16•3, 75=25•3, 12=4•3 that means
√147=7√3, √108=6√3, √48=4√3, √75=5√3, √12=2√3
perimeter=3•7√3+2•6√3+2•4 √3+3•5√3+6•2√3=68√3
Square:
4•1/3•√63=4/3•√9•√7=4√7
Rectangle:
2•1/4√100+2(2√48+4√75)=
5+2(8√3+20√3)=5+56√3
Now, if you use a calculator, you will find that the greatest perimeter is for the triangle shape.