Question

The perimeter of a rectangle is 44 cm. If one of the two adjacent sides is 1.8 cm longer than the other, what are the lengths of the sides?​

Answer 1

$\mathcal{ \underline{Given:- }}$

$• \sf \: The \: perimeter \: of \: a \: rectangle \: is \: 44 \: cm.$

$• \sf \: One \: of \: the \: two \: adjacent \: sides \: is \: 1.8 \: cm \: longer \: than \: the \: other.$

$\mathcal{\underline{To \: Find :- }}$

$• \sf \: The \: lengths \: of \: the \: sides.$

$\huge \mathcal{ \underline{Solution :- }}$

$\sf{We \: know \: that, }$

$\bf \red{ \star \: {Perimeter \: of \: a \: rectangle \: = \: 2 (length + breadth) \: unit}}$

$\sf{According \: to \: the \: question, }$

$\sf\: {Let \: the \: length \: be \: x \: cm }$

$\therefore \sf breadth \: will \: be \: (x + 1.8) \: cm$

$\therefore \sf44 = 2(x + x + 1.8)$

$\rightarrow \sf44 = 2(2x + 1.8)$

$\rightarrow \sf22 = 2x + 1.8$

$\rightarrow \sf2x + 1.8 = 22$

$\rightarrow \sf2x = 20.2$

$\rightarrow \sf x= 10.1$

$\sf \pink{Therefore, \: length \: is \: 10.1 \: cm \: and}$

$\sf \pink{breadth \: is \: (10.1 + 1.8) \: cm = 11.9 \: cm}$

$\bf \underline{Correction \: Test}$

$\sf{Perimeter \: of \: the \: rectangle =2(10.1 + 11.9) \: cm }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =( 2 \times 22) \: cm$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =44 \: cm$

$\bf{Hence, Answers \: are \: 10.1 \: cm \: and \: 11.9 \: cm. }$

Answer 2

Given

Perimeter of Rectangle=44cm

One side is 1.8cm longer than the other side

To Find

Length of the sides

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf According \:to \:the \:question$

Let the one side of Rectangle be 'x'

and the other be 1.8+x[given]

$\sf\boxed{\bold {Perimeter \:of \:Rectangle \:=2(length+breadth)}}$

$\sf \longmapsto 44=2[x+(1.8+x)]$

$\sf \longmapsto44=2(2x+1.8)$

$\sf\longmapsto22=2x+1.8$

$\sf \longmapsto22-1.8=2x$

$\sf\longmapsto 2x=20.2$

$\sf\large \bold{x=10.1}$

$\sf Other \:side =1.8+x=1.8+10.1=11.9$

∴length is $\bold{\red{11.9 cm}}$

breadth is $\bold{\red{10.1 cm}}$

Check

$\sf Perimeter \:of\: Rectangle =2(l+b)$

$\sf\longmapsto2(10.1+11.9)$

$\sf \longmapsto2(22)$

$\sf\longmapsto44$