Problem of the Week
Problem B and Solution
Skott’s Spots
Problem
Skott was painting the walls in his living room and den. Unfortunately, he
accidentally got some small dots of paint on the ceiling near the wall. So he
decided to put a decorative rope along the ceiling, where it meets the walls.
To do this, Skott has to measure the perimeter of the ceilings to make sure he has
enough of the decorative rope to go around each ceiling.
Both ceilings have an area of 24 square metres, with dimensions that are whole
numbers.
Skott realizes that his 20 m roll of decorative rope is only enough for one ceiling
but not the other.
a) Find the dimensions of the room for which Skott has enough decorative rope.
b) Given that the other room has different dimensions, and its perimeter is less
than 50 m, how much more decorative rope does he need to ensure he can do
the other room?
Solution
a) From the table at the right, we see that
the only room of area 24 m2 for which
Skott has enough decorative rope is one
that is 4 m by 6 m.
b) Given that its perimeter is less than 50 m
and its dimensions are different than the
other room, the other room could have
dimensions of either 3 m by 8 m or 2 m by
12 m, with perimeters of 22 m and 28 m
respectively. Thus to ensure he can do
the other room, Skott needs 28 m more of
the decorative rope.
For rooms of area 24 m2 :
Dimensions
Perimeter
1 × 24
50
2 × 12
28
3×8
22
4×6
20