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# The width of a rectangle is 31 centimeters. Find all possible values for the length of the rectangle if the perimeter is al least 692 centimerts

I am trying to pull out equations from word problems

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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P = 2L + 2W

P ≥ 692

L+ W ≥ 346

L+31≥ 346

L ≥315

This is simply an inequality problem.( ≥ ) should be used for at least ( minimum value),

Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
4.6 4.6 (8 lesson ratings) (8)
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In a rectangle opposite sides are equal

perimeter = 2(length + Width)

2(l + W) must greater than or equal to 692
L + W must be greater than or equal to (692/2)346
L + 31 must be greater than or equal to 346
there fore L must be greater than or equal to (346 - 31) 315
:)

Michael W. | Experienced Biology teacher/tutor/nestorExperienced Biology teacher/tutor/nestor
5.0 5.0 (345 lesson ratings) (345)
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Good morning! Recall that perimeter of a rectangle is the sum of the lengths of all sides, so:

P= L + L + W + W, or P + 2L + 2W

If the width is 31 and total perimeter is at least 692, then the minimum would be:

692 = 2L + 2(31), or 692 = 2L + 62

Subtract 62 from both sides:

630 = 2L

Divide both sides by 2:

315 = L

Remember that the perimeter is at least 692; therefore the length would be at least 315 cm

Hope this helps

Mike