Respuesta :

Given :

  • The Perimeter of the rectangle is 60 cm
  • The ratio of the length to the width is 3:2.

To Find :

  • The Length and width of the rectangle .

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Solution :

We know that,

[tex]\qquad{ \bold{ \pmb{2(Length + Breadth ) = Perimeter_{(rectangle)}}}}[/tex]

Let's assume the length of the rectangle as 3x inches. and the width is 2x inches.

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Now, Substituting the given values in the formula :

[tex]\qquad \dashrightarrow{ \sf{2(3x + 2x )= 60}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{2(6x)= 60}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{12x= 60}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{x= \dfrac{60}{12} }}[/tex]

[tex]\qquad \dashrightarrow{ \bf{x= 5}}[/tex]

Therefore,

[tex]\qquad { \pmb{ \bf{ Length _{(rectangle)} = 3x \: = 3(5) = 15 \: inches}}}\:[/tex]

[tex]\qquad { \pmb{ \bf{ Width _{(rectangle)} = 2x = 2(5) = 10 \: inches}}}\:[/tex]