Junior Category: Fair and Square
Alex, Ben and Charlie need several square bits of paper for a collage they plan to make. They
have the following rectangular sheets of paper.
Alex has a 15 cm x 12 cm sheet.
Ben has a 7.5 cm x 12 cm sheet.
Charlie has a 15 cm x 6 cm sheet.
Each person cuts his sheet into square pieces such that:
The entire sheet is used (that is, no non-square pieces of paper are left over)
The smallest possible number of square pieces are formed from each sheet
Who cuts out the least number of squares?
Option 1: Alex
Option 2: Ben
Option 3: Charlie
Option 4: They all cut out the same number of squares
Answers
Given : Alex has a 15 cm x 12 cm sheet. , Ben has a 7.5 cm x 12 cm sheet.
Charlie has a 15 cm x 6 cm sheet. Each person cuts his sheet into square pieces such that: The entire sheet is used , The smallest possible number of square pieces are formed from each sheet
To find : Who cuts out the least number of squares
Solution
As least number of squares are cut , hence we need to find HCF to find size of square cut
Alex has a 15 cm x 12 cm sheet.
HCF = 3
Alex cut squares = 3 * 3
Number of alex square = 15 * 12 / (3 * 3) = 20
Ben has a 7.5 cm x 12 cm sheet.
7.5 = 15/2
HCF = 3/2 = 1.5
Ben cut square = 1.5 * 15
Number of Ben Squares = 7.5 * 12/ (1.5 * 1.5) = 40
Charlie has a 15 cm x 6 cm sheet.
HCF = 3
Charlies cut square = 3 * 3
Number of charlie squares = 15 * 6 / ( 3 * 3) = 10
charlie cuts out the least number of squares
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