Mathematics

Question

The length of a rectangle envelope is 2 1/2 times its width. A plastic band surrounds the front and back of the envelope to secure it as shown in the picture. The plastic band is 39 3/8 inches long. Find the length and width of the envelope.

1 Answer

  • Answer:

    Length of the envelope = 14

    Width of the envelope = 5.6

    Step-by-step explanation:

    Let the width of the rectangle be  x

    Then the length of the rectangle will be [tex]2\frac{1}{2} \times x[/tex]

    Also the length of the plastic band to cover the  front and back of the envolpe =  [tex]39\frac{3}{8}[/tex]

    To cover one side th band required is

    =>[tex]\frac{39\frac{3}{8}}{2}[/tex]

    =>[tex]\frac{\frac{315}{8}}{2}[/tex]

    =>[tex]\frac{\frac{315}{8}}{2}[/tex]

    =>[tex]{\frac{315}{16}[/tex]

    =>39.4

    We know that the perimeter of the rectangle is

    => 2( L + B) = [tex]{\frac{39.4}{2}[/tex]

    => 2( [tex]2\frac{1}{2} \times x + x[/tex]) = 19.7

    => 2( [tex]\frac{7}{2}x) = 19.7 [/tex]

    =>  [tex]3.5x = 19.7 [/tex]

    => [tex] x = \frac{19.7}{3.5} [/tex]

    =>  [tex]x = 5.6[/tex]

    Now length of the envelope =

    =>  [tex]2\frac{1}{2} \times x [/tex]

    =>  [tex] 2.5 \times 5.6 [/tex]

    => 14

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