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A frame around a rectangular family portrait has a perimeter of 138 inches. The length is nine more than three times the width. Find the length and width of the frame.

Respuesta :

Given :

  • Perimeter of the frame is 138 inches.
  • The length is nine more than three times the width

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To Find :

  • The Length and width of the frame .

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Solution :

We know that,

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

Let's assume the width of the rectangle as x inches. Then the length will become (3x + 9).

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Now, Substituting the given values in the formula :

[tex]\qquad \dashrightarrow{ \sf{2(3x + 9 + x )= 138}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{2(4x + 9 )= 138}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{8x + 18= 138}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{8x = 138 - 18}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{8x = 120}}[/tex]

[tex]\qquad \dashrightarrow{ \sf{x = \dfrac{120}{8} }}[/tex]

[tex]\qquad \dashrightarrow{ \bf \: x = 15}[/tex]

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Therefore,

[tex]\qquad { \pmb{ \bf{ Width _{(frame)} = x = 15 \: inches}}}\:[/tex]

[tex]\qquad { \pmb{ \bf{ Length _{(frame)} = (3x + 9) \: = 3(15) + 9 = 54 \: inches}}}\:[/tex]

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