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April 5th, 2007, 04:08 PM  #1 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  Percent of Square's Area
If the length of each side of a square is increased by 10%, by what percent does the area of the square increase? MY WORK: A = side^2 A = (0.10)^2 A = 0.20 Area is increased by 20%. However, the textbook tells me that the correct answer is 21%. How can this be? 
April 5th, 2007, 05:08 PM  #2 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0 
A = side^2 new side = old side + 0.1*old side = 1.1*old side A = (1.1(s))^2 A = (1.21)s^2 Since s^2 was the old area, the new area is 21% greater than the old area. Area is increased by 21%. 
April 5th, 2007, 05:18 PM  #3 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  ok
Where did you get 1.1?

April 5th, 2007, 05:23 PM  #4 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0 
Because the new side is 10% longer than the old side. So, the new side is equal to the (old side + 0.1*old side), since (0.1*old side) = 10% of the old side.

April 5th, 2007, 05:30 PM  #5 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  ok
This is a tricky question. All this new side versus the old side. 
April 6th, 2007, 09:32 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
If the length of each side of a square is increased by 10%, what makes you think the result is a square? Nothing in the question tells you that.

April 6th, 2007, 09:50 AM  #7 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0 
Why wouldn't the result be a square?

April 6th, 2007, 02:19 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
What is there to "hold the square together"?

April 6th, 2007, 02:23 PM  #9 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0 
True. However, if we specified that one corner of the square held intact, and that the sides that grew were at right angles to each other, and the square was redrawn from there, that would better represent this situation.

April 6th, 2007, 02:34 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
Okay  so your viewpoint is now one corner and angles are maintained. What holds the opposite corner together?


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area, percent, square 
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