Question

The length of a fild exceeds its breadth by 5 metre. If the breadth be increased by 12 metre and length is decreased by 5 , then the area of the field is increased by 140m squar afind the length and breadth of the field

Answer 1

$\sf\large{Given:}$

• $\sf{The\: length\:of\:a\: field\: exceeds\: it's\: breadth\:by\:5\:m}$
• $\sf{If\: breadth\:is\: increased\:by\:12m\:and\: length\:is\: decreased\:by\:5m}$
• $\sf{The\: area\:of\: field\:is\: increased\:by\:140m^2}$

$\sf\large{Let:}$

• $\sf{The\: length\:of\: field=l+5}$
• $\sf{The\: breadth\:of\: field=l}$

$\sf\large{Solution:}$

$\sf{According\:to\:1st\:case:}$

$\rm{\implies Area=l*b}$

$\rm\red{\implies (l+5)(l)}$

$\rm\red{\implies l^2+5l}$

$\sf{According\:to\:2nd\:case:}$

$\sf{\implies Area\:of\: field=l*b}$

$\rm{\implies Area=(l+5-5)(l+12)}$

$\rm{\implies Area=l(l+12)}$

$\rm{\implies l^2+12l}$

• $\sf{Now,\: solving\: here}$

$\rm{\implies Case_2=Case_1+140}$

$\rm{\implies (l^2+12l)=(l^2+5l)+140}$

$\rm{\implies l^2+12l-l^2-5l=140}$

$\rm{\implies 7l=140}$

$\rm{\implies l=20m}$

• $\sf{putting\: value\:l=20\:to\: find\: length\:and\: breadth}$

$\sf{\implies The\: length\:of\: field=20+5=25m}$

$\sf{\implies The\: breadth\:of\: field=l=20m}$

Hence,

$\sf\large\red{\implies The\: length\:of\: field=25m}$

$\sf\large\purple{\implies The\: breadth\:of\: field=20m}$

Answer 2

The length of a fild exceeds its breadth by 5 metre. If the breadth be increased by 12 metre and length is decreased by 5 , then the area of the field is increased by 140m squar afind the length and breadth of the field

by find we get

length of the field=25m

breadth of the field=20m