Hally A.

asked • 11/27/15

find the length and width of the envelope

the length of a rectangular envelope is 2 1/2 times  its width. A plastic band surrounds the front and back of the envelope to secure it. the plastic band is 39 3/8 inches long.  find the length and width of the envelope.  
 

Norbert J. M.

tutor
Please describe what is being shown in the picture to the band to secure the envelope.
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11/27/15

Andrew M.

It appears we are to assume the envelope is "flat" so there
is no 3rd dimension involved.
 
If the band encircles the envelope and is 39 3/8 inches then
one dimension is (1/2)(39 3/8) or 315/4 inches = 78 3/4 inches.
 
My question is whether you are considering that dimension
to be the length or the width??
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11/28/15

Norbert J. M.

tutor
It is possible that plastic band may occur on an angle creating triangles on each of the opposite corners on opposite sides.  More information is needed.
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11/28/15

1 Expert Answer

By:

Don L. answered • 11/28/15

Tutor
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Fifteen years teaching and tutoring basic math skills and algebra
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Hi Hally, let x represent the width of the envelop. Then the length is 2 and 1 / 2 times x. If the band going around the envelop is 39 and 3 / 8 inches, we can find the width of the envelop.
 
We will discount any thickness in the envelop. That means one half of the band covers the front of the envelop and one half covers the back.
 
Find one half of band:
 
Change the mixed fraction 39 and 3/8 to an improper fraction.
 
((39 * 8) + 3) / 8 = 315 / 8
 
Divide  by 2:
 
(315 / 8) / 2 = 315 / 16 = 19 and 11 / 16
 
The width of the envelop is 19 and 11 / 16 inches.
 
The length is 2 and 1 /2 times the width.
 
5 / 2 * 315 / 16 = 1575 / 32 = 49 and 7 / 32
 
The length of the envelop is 49 and 7 / 32 inches.
 
Questions?
 
 
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Norbert J. M.

tutor
Alternate solution:  If band is parallel to the longest dimension "L".
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11/28/15

Don L.

tutor
Hi Norbert, good point. If the band was parallel to the length, then the length of the envelop would be 19 and 11 / 19 inches in length.
 
Since the length is 2 and 1 / 2 times the width, the width would be 7 and 7 / 8 inches.
 
Questions?
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11/28/15

Frankellys S.

If the band that goes around the envelope is  39 3/8 inches how is the length(49 7/32) Of the envelope going to be more than band that goes around the envelope? 
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02/28/16

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