Question

Quadrilateral EFGH is a rectangle. if EF = 4x - 12, HG=2x + 6 , and FG = 2x , find its perimeter.

Answer 1

let us illustrate it first...

Answer 2

since this is a rectangle, all 4 angles are equal, then parallel sides are equal such that EF=HG, as well as EH=FG....
so for EF=HG
4x-12=2x+6
4x-2x=12+6 by transposition
2x=18
x=18/2 by cross-multiplication
x=9

Answer 3

therefore the long side EF or HG is...
EF=4(9)-12=36-12=24
HG=2(9)+6=18+6=24

Answer 4

the shorter side FG=2x, then
FG=2(9)=18
EH=FG=18

Answer 5

the perimeter then is...
P=EF+HG+2(FG)
P=24+24+2(18)
P=48+36
P=84 units