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.

Answer 1

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 $2\frac{1}{2} \times x$

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

To cover one side th band required is

=>$\frac{39\frac{3}{8}}{2}$

=>$\frac{\frac{315}{8}}{2}$

=>$\frac{\frac{315}{8}}{2}$

=>${\frac{315}{16}$

=>39.4

We know that the perimeter of the rectangle is

=> 2( L + B) = ${\frac{39.4}{2}$

=> 2( $2\frac{1}{2} \times x + x$) = 19.7

=> 2( $\frac{7}{2}x) = 19.7$

=>  $3.5x = 19.7$

=> $x = \frac{19.7}{3.5}$

=>  $x = 5.6$

Now length of the envelope =

=>  $2\frac{1}{2} \times x$

=>  $2.5 \times 5.6$

=> 14