Question

Which geometric figure has the greatest perimeter?

The Square
The right triangle
The rectangle

Answer 1

Triangle has the greatest perimeter

Explanation:

Triangle:

`2√(48)=2√(2*2*2*2*3)=2*2*2√(3)=8√(3)\\\\\\3√(75)=3*√(3*5*5)=3*5*√(3)=15√(3)\\\\\\6√(12)=6*√(2*2*3)=6*2*√(3)=12√(3)\\\\\\2√(108)=2*√(2*2*3*3*3)=2*2*3*√(3)=12√(3)\\\\\\3√(147)=3*√(3*7*7)=3*7√(3)=21√(3)\\\\Perimeter=3√(147)+2√(108)+6√(12)+2√(48)+3√(75)\\\\ =21√(3)+12√(3)+12√(3)+8√(3)+15√(3)\\\\=(21+12+12+8+15)√(3)\\\\=68√(3)\\`

= 68 * 1.732 = 117.78

Square:

`(1)/(3)√(63)=(1)/(3)√(3*3*7)=(1)/(3)*3*√(7)=√(7)\\\\Perimeter=4*side=4*√(7)=4√(7) = 4* 2.6458 = 10.58`

Rectangle:

`(1)/(4)√(100)=(1)/(4)√(10*10)=(1)/(4)*10=(5)/(2)\\\\\\Perimeter=(1)/(4)√(100)+2√(48)+4√(75)+(1)/(4)√(100)+2√(48)+4√(75)\\\\=(5)/(2)+8√(3)+20√(3)+(5)/(2)+8√(3)+20√(3)\\\\=(5+5)/(2)+(8+8+20+20)√(3) \\\\=(10)/(2)+56√(3)+\\\\=5+56√(3)\\\\=5+56*1.732=5+96.99=102`