Perimeter of square = 48 m. Small bed covers 18 sq m. Find area not covered, fraction, and ratio.
Not covered = 198 m²
Fraction = 18/216 = 1/12
Ratio = 1:11
Step 1: Find the side of the square.
Perimeter of a square = (4 imes ext{side}).
So, ( ext{side} = dfrac{48}{4}).
( ext{side} = 12 ext{m}).
Step 2: Find the total area of the square (the room).
Area of a square = ( ext{side} imes ext{side}).
(= 12 imes 12).
(= 144 ext{m}^2).
Step 3: Use the bed’s area.
Given: bed covers (18 ext{m}^2).
Step 4: Area not covered by the bed.
( ext{uncovered area} = ext{total area} - ext{covered area}).
(= 144 - 18).
(= 126 ext{m}^2).
Step 5: Fraction of the room that is covered.
(dfrac{ ext{covered}}{ ext{total}} = dfrac{18}{144}).
Divide top and bottom by (18): (dfrac{1}{8}).
(Optional, for clarity) Fraction not covered:
(dfrac{126}{144} = dfrac{7}{8}) after dividing by (18).
Step 6: Ratio of covered area to uncovered area.
( ext{covered}: ext{uncovered} = 18:126).
Divide both by (18): (1:7).
Final Answers:
Area not covered = (126 ext{m}^2).
Fraction covered = (dfrac{1}{8}).
Ratio (covered : uncovered) = (1:7).