contestada

The perimeter of the rectangle is 98 inches The ratio of the length to the width is 4:3. What is the length and the width of the rectangle

Respuesta :

Given :

  • The Perimeter of the rectangle is 98 inches
  • The ratio of the length to the width is 4:3.

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 4x inches. and the width is 3x inches.

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Now, Substituting the given values in the formula :

[tex]\qquad \dashrightarrow{ \sf{2(4x + 3x )= 98}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{2(7x)= 98}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{14x= 98}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{x= \dfrac{98}{14 } }}[/tex]

[tex]\qquad \dashrightarrow{ \bf{x= 7}}[/tex]

Therefore,

[tex]\qquad { \pmb{ \bf{ Length _{(rectangle)} = 4x \: = 4(7) = 28 \: inches}}}\:[/tex]

[tex]\qquad { \pmb{ \bf{ Width _{(rectangle)} = 3x = 3(7) = 21 \: inches}}}\:[/tex]