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. T
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1 Answer

1. User Answers nandhini123
Answer:
Length of the envelope = 14
Width of the envelope = 5.6
Stepbystep 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