SOLUTION: The width (w) of a rectangle is two less than 1/3 of its length (l). If the perimeter is 116 cm. identify the equation of the problem

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Question 976555: The width (w) of a rectangle is two less than 1/3 of its length (l). If the perimeter is 116 cm. identify the equation of the problem
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Made more general,
The width (w) of a rectangle is k less than n/d of its length (L). If the perimeter is p cm. identify the equation of the problem.

2w%2B2L=p

Description means w=-k%2B%28n%2Fd%29L or w=%28n%2Fd%29L-k.

Returning to the perimeter equation and substituting for w,
2%28%28n%2Fd%29L-k%29%2B2L=p

2nL%2Fd-2k%2B2L=p

2nL%2Fd%2B2L-2k=p

%282n%2Fd%2B2%29L-2k=p-----this may be one of your choices if keeping completely in symbolic form.

You can solve the equation for L, one of the unknown quantities.
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%282n%2Fd%2B2%29L=p%2B2k

%28%282n%2B2d%29%2Fd%29L=p%2B2k

highlight_green%28L=%28p%2B2k%29%28d%2F%282n%2B2d%29%29%29

That form for L might be fairly convenient to use. You can substitute as variables were assigned:
system%28n=1%2Cd=3%2Cp=116%2Ck=2%29;
Evaluate L...

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The width (w) of a rectangle is two less than 1/3 of its length (l). If the perimeter is 116 cm. identify the equation of the problem
Let length be L, and width, W

Then W = L%2F3+-+2

2(L + W) = perimeter

2(L + W) = 116

2(L + W) = 2(58)

L + W = 58

L+%2B+L%2F3+-+2+=+58 ------ Substituting L%2F3+-+2 for width

highlight_green%28L+%2B+L%2F3+=+60%29 ------ Required equation