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  • What is the smallest number of 6 cm by 8 cm rectangles which can be fitted together to make a large rectangle with sides in the ratio 5?3 ?

What is the smallest number of 6 cm by 8 cm rectangles which can be fitted together to make a large rectangle with sides in the ratio 5?3 ?

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Let;us;arrange;the;small;rectangles;6;cm; imes8;cm;all;side;by;side.\*Let;M;of;them;be;kept;side;by;side;with;6;cm;facing;outside.\*So;a;rectangle;of;length;6;M;cm;and;width;8;cm;is;formed.\* Let;us;arrange;N;rows;of;them.;Thus;a;rectangle;is;formed;with; dimensions:;6;M;cm imes 8;N;cm.\*These;dimensions;are;in;the; ratio;5:3;or;3:5.\* extbfCase;1:6;M:8;N=5:3\*fracMN=frac53 imes frac86=frac209\*9;M=20;N\*As;M;and;N;are;integers,; the;minimum;values;for;which;the;above;equation;is*;satisfied,;is:; N=9;and;M=20.\*So,;the;total;number;of;small;rectangles=M imes N=180\* extbfCase;2:6;M:8;N=3:5\*fracMN=frac2430=frac45\* So,;for ;minimum ;integer;values;of;M;and;N,;are; M=4;and;N=5\*the;total;number ;of ;small; rectangles=4 imes 5=20.

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Deependra Verma

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