Question

if the length is increasing by 2m and breath is by 3m then the area of rectangular floor of rafique is increasing by 75 sq m .but if the length is reduced by 2m and breath is increased by 3m the area is increased by 15 sq m .by forming simultaneously linear equation let us determine the length and breadth of the floor how to find the equation of this question​
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Answer 1

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$\sf let \: the \: length \: be \:L m \: and \:breadth \: be \:b \: m$

$\sf so, \: the \:area \: is = Lb \:sq.m$

$\sf in \:case- I$

$\sf increased \: length= L+2$

$\sf increased \: breadth = b+3$

$\sf increased \:area = Lb+75$

$\sf\blue{To \: be \: noted:}$

$\sf {\boxed {\bf Length(L) {\bf × {\bf breadth (b) {\bf = {\bf area(Lb)}}}}}}$

$\sf (L+2)(b+3)=Lb+75$

$\sf Lb + 3L+ 2b+6=Lb+ 75$

$\sf Lb-Lb +3L+2b+6-75=0$

$\sf 3L+2b-69=0-------equation \: l$

$\sf in case- ll$

$\sf reduced \:length= L-2$

$\sf increased \: breadth = b+3$

$\sf increased \:area = Lb+15$

$\sf {\boxed {\bf Length(L) {\bf × {\bf breadth (b) {\bf = {\bf area(Lb)}}}}}}$

$\sf (L-2)(b+3)=Lb+15$

$\sf Lb+3L-2b-6=Lb+15$

$\sf Lb-Lb+3L-2b-6-15=0$

$\sf 3L-2b-21=0 -------- equation \:ll$

$\sf from \:both \: equations \: l \: and \:ll$

$\sf 3L+2b-69=0$

$\sf 3L-2b-21=0$

$\sf - \: + \: +$

_________$\sf (by \: subtracting)$

$\sf 0×3L+4b-48=0$

$\sf 4b=48$

b$\ = \dfrac{48}{4}$

$\sf b= 12$

$\sf putting \: the \: value \: of \:b \: in \:equation \: l$

$\sf 3L+2×12-69=0$

$\sf 3L+24-69=0$

$\sf 3L-45=0$

$\sf 3L=45$

L$\ = \dfrac{45}{3}$

$\sf L=15$

$\sf therefore, \: length \: is \:= \:15m \: and \:Breadth \: is \: = \: 12 \: m$

Answer 2

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