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the perimeter of the rectangle is 88 the etive more than twice width find the length and the width

Sagot :

Starrysoul100

[tex]\bold{\boxed{\huge{\blue{\underline{Answer }}}}}[/tex]

[tex]\bold{\underline{Given :- }}[/tex]

[tex]\sf{The \: perimeter\:of\:the\:rectangle = 88}[/tex]

[tex]\sf{The \: length \: is\: 5 \:more \:than \: 2 × width }[/tex]

[tex]\bold{\underline{To \: Find :- }}[/tex]

  • We have to find the length and breath of the rectangle .

[tex]\bold{\underline{Let's \:Begin :- }}[/tex]

[tex]\sf{ Let\: the\: breath \:be \: x }[/tex]

[tex]\sf{\underline{ We\: know\: that, }}[/tex]

[tex]\sf{\red{ Perimeter\: of \: rectangle = 2( L + W)}}[/tex]

[tex]\sf{\underline{ According\: to\: the \:question }}[/tex]

[tex]\sf{The \: length \: is \: 5 \:more \:than \: 2 × width }[/tex]

[tex]\sf{\underline{That \:is }}[/tex]

[tex]\sf{ Length = 2x + 5 }[/tex]

[tex]\sf{\underline{Subsitute the \:required \:values }}[/tex]

[tex]\sf{ Perimeter \:of\: rectangle = 2( L + W) }[/tex]

[tex]\sf{ 88 = 2( 2x + 5 + x) }[/tex]

[tex]\sf{ 88 = 4x + 10 + 2x }[/tex]

[tex]\sf{ 88 = 6x + 10 }[/tex]

[tex]\sf{ 88 - 10 = 6x }[/tex]

[tex]\sf{ 78 = 6x }[/tex]

[tex]\sf{ x = 78/6 }[/tex]

[tex]\sf{ x = 13 }[/tex]

[tex]\sf{ Thus,\: the \:width \:is \:13\: feet }[/tex]

[tex]\bold{\underline{ Now }}[/tex]

[tex]\sf{ Length = 2x + 5 }[/tex]

[tex]\sf{ Length = 2(13) + 5 }[/tex]

[tex]\sf{ Length = 26 + 5 }[/tex]

[tex]\sf{ Length = 31 }[/tex]

[tex]\sf{\pink{ Hence, \: Length\: and \:breath \:are\: 13 \:and\: 31 \: feet}}[/tex]

Correct Question:-

The length is 5more than twice the width.

Solution:-

  • Let width be x
  • Length be 2x+5

ATQ

[tex]\\ \tt\hookrightarrow 2(L+B)=88[/tex]

[tex]\\ \tt\hookrightarrow 2(x+2x+5)=88[/tex]

[tex]\\ \tt\hookrightarrow 2(3x+5)=88[/tex]

[tex]\\ \tt\hookrightarrow 6x+10=88[/tex]

[tex]\\ \tt\hookrightarrow 6x=78[/tex]

[tex]\\ \tt\hookrightarrow x=13[/tex]

  • Width=13
  • Length=2(13)+5=31
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