My Math Forum Percent of Square's Area

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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 re-drawn 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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# each side of a square is increased by 10

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