Question

The length of a rectangular field is 6 m less than thrice its breadth and the area of the field is 360 m². The breadth of the field is_________ m​

Answer 1

Answer:

400msquare...................

Answer 2

Solution :

Let the length of rectangular field be r & the breadth of rectangular field be m.

A/q

$\longrightarrow\sf{r=2m-6......................(1)}$

We know that formula of the area of rectangle :

$\boxed{\bf{Area=Length\times breadth\:\:\:\:(sq.unit)}}}}$

$\longrightarrow\sf{r\times m=360}\\\\\longrightarrow\sf{(2m-6)m=360\:\:[from(1)]}\\\\\longrightarrow\sf{2m^{2} - 6m =360}\\\\\longrightarrow\sf{2m^{2}-6m-360=0}\\\\\longrightarrow\sf{2(m^{2}-3m-180)=0}\\\\\longrightarrow\sf{m^{2}-3m-180=\cancel{0/2}}\\\\\longrightarrow\sf{m^{2}-3m-180=0}\\\\\longrightarrow\sf{m^{2}+12m-15m-180=0}\\\\\longrightarrow\sf{m(m+12)-15(m+12)=0}\\\\\longrightarrow\sf{(m+12)(m-15)=0}\\\\\longrightarrow\sf{m+12=0\:\:Or\:\:m-15=0}$

$\longrightarrow\bf{m\neq -12\:m\:\:Or\:\:m=15\:m}$

We know that negative value isn't acceptable .

Thus;

$\boxed{\sf{The\:breadth\:of\:the\:field\:is\:=\boxed{\bf{15\:m}}}}}\\\boxed{\sf{The\:Length\:of\:the\:field\:is\:=(2m-6)=(2\times 15-6)=30-6=\boxed{\bf{24\:m}}}}}$