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Problem of the Week
Problem C and Solutions
Framed
Problem
Four rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged
to form the outer section of a picture frame, as shown. Determine the area
inside the wooden frame.
Solution 1
The inner square has side length 30 − 3 = 27 cm.
Area = Length × Width = 27 × 27 = 729 cm2 .
30
27
Therefore, the enclosed area is 729 cm2 .
3
Solution 2
3
Each rectangle has area 30 × 3 = 90 cm2 .
The outer square has a side length equal to
30 + 3 = 33 cm.
33
30
The area of the outer square is therefore
33 × 33 = 1089 cm2 .
The area of the inner square is equal to the area
of the outer square minus the areas of the four
rectangles.
30
3
Therefore, the area of the inner square is 1089 − 4 × 90 = 729 cm2 .
33