SOLUTION: A rectangular piece of fabric is 4 times as long as its width. If it is 25% shorter and 200% wider, it will become a square piece of fabric with an area of 36 m2. What are the dime

Question 1189257: A rectangular piece of fabric is 4 times as long as its width. If it is 25% shorter and 200% wider, it will become a square piece of fabric with an area of 36 m2. What are the dimensions of the piece of fabric?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

I'm quite astonished by this problem. The statement of the problem is 100% correct both grammatically and mathematically. That is almost NEVER the case when a phrase like "200% wider" is used.

I applaud the author of the problem for using correct English!

"A rectangular piece of fabric is 4 times as long as its width."

Let the width be x; then the length is 4x.

"If it is 25% shorter and 200% wider..."

25% shorter means 75% as long; 75% of 4x is 3x.

200% wider means the width is INCREASED by 200%, which means it becomes 100%+200% = 300% AS WIDE, or 3 times AS WIDE as it was; 3 times x is 3x.

"...it will become a square piece of fabric..."

Indeed it will be -- the length and width are both 3x.

"... with an area of 36 m^2"

(obviously we reject the solution x=-2, since it makes no sense as the width of the piece of fabric)

ANSWERS: width = x = 2m; length = 4x = 8m

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