width = 5m
Step-by-step explanation:
Length of room = 2m longer than width
length = 2m + width
Perimeter = 24 meters
The room will be rectangular since width and length are not the same
The formula for perimeter of a rectangle:
Perimter = 2(length + width)
24 = 2[(2m + width) + width)
24 = 2( 2m + width + width)
24 = 2(2 + 2width)
24 = 4 + 4 width
subtract 4 from both sides:
24 - 4 = 4 - 4 + 4 width
20 = 4 width
divide both sides by 4:
20/4 = 4 width/4
width = 5
width = 5 m
length = 2m + width
length = 2m + 5m = 7m
To check:
perimter = 2(7 + 5) = 2(12) = 24
24 = 2