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Problem of the Week
Problem B and Solution
Wrecked-Angle
Problem
The area of a rectangle is equal to the product of its length times its width.
a) What are the possible dimensions of a rectangle of area 60 cm2 ? Fill in the
first two columns of the given table, using width as the lesser dimension and
length as the greater.
b) Which of these possible rectangles, if its length is decreased by 4 cm and its
width is increased by 1 cm, would result in a rectangle four times as long as
it is wide? Complete the table to help find the answer.
Solution
Here is the completed table.
Table of Dimensions (all measurements in cm)
Width
Length
Width + 1
Length − 4
1
60
2
56
2
30
3
26
3
20
4
16
4
15
5
11
5
12
6
8
6
10
7
6
a) The first two columns reveal the six possible sets of dimensions.
b) The third row of the table shows that the 3 cm by 20 cm rectangle, upon
increasing its width to 4 cm and decreasing its length to 16 cm, gives a
rectangle with length four times its width.