SOLUTION: the lenght of the rectangle is 5 cm less then twice the width. if the perimeter is greater than 36 cm but less than 50cm, What is the longest possible lenght of the rectangle?

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Question 889573: the lenght of the rectangle is 5 cm less then twice the width. if the perimeter is
greater than 36 cm but less than 50cm, What is the longest possible lenght of the
rectangle?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = width and L = length.
L=2w-5 and 50%3E2w%2B2L%3E36.

Wanting the longest length, first solve for w in terms of L.
2w=L%2B5
w=%28L%2B5%29%2F2, and substitute this into the inequality.

50%3E2%28L%2B5%29%2F2%2B2L%3E36
50%3EL%2B5%2B2L%3E36
50%3E3L%2B5%3E36
50-5%3E3L%3E36-5
45%3E3L%3E29
29%2F3%3CL%3C45%2F3
highlight%2829%2F3%3CL%3C15%29

For the LONGEST possible rectangle, L can be as near to 15 as desired but still must be less than 15. A suitable value for w can then be found in order to agree with the inequality.