Question

If the area of a rectangular field is $3600$ square units and the length and breadth of the field are coprime to each other, then the possible value of length(s) is (are)

• A. $144$
• B. $150$
• C. $180$
• D. $225$

Answer 1

Answer: (A), (D)

The correct options are
A $144$
D $225$

Area $=3600=2^4\cdot 3^2\cdot 5^2$
Since, the length and breadth of the field are coprime to each other then the possibilities are
$l\times b=(2^4\cdot 3^2)\times 5^2=144\times 25$
Or $l\times b=(2^4\cdot 5^2)\times 3^2=400\times 9$
Or $l\times b=(3^2\cdot 5^2)\times 2^4=225\times 16$

So, the length can be $144,225,400$ units.