document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96231>Question 96231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help again!  It seems there are different ways to figure out problems for rectangles, squares, and triangles.  Is there a different formula for all of them.  The questions I'm working with give me the perimeter I have to figure out the dimensions. I FEEL SO OVERWHELMED!\r<BR>\n" );
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document.write( "ex. A square has a perimeter of 28 feet.  Find the length of each side.\r<BR>\n" );
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document.write( "ex. A triangle has a perimeter of 23 inches. The medium side is 3 inches more than the shortest side, and the longest side is twice the shortest side.  Find the shortest side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70053 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=70053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Whenever you feel overwhelmed, you should always try to go back to the basic things you <BR>\n" );
document.write( "have learned. For example, these two problems involve perimeters. You should know that, by<BR>\n" );
document.write( "definition, the perimeter of a geometric figure is just the sum of the lengths of all the sides.<BR>\n" );
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document.write( "The first problem involves the perimeter and a square. What do you know about squares? A square<BR>\n" );
document.write( "is a special case of a rectangle. It has four sides and 4 angles of 90 degrees. In addition,<BR>\n" );
document.write( "what makes a square different from most rectangles? You probably know that all the sides<BR>\n" );
document.write( "of a square are equal. Let's use this basic information to solve the first problem.<BR>\n" );
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document.write( "Since the perimeter of a four sided figure is the sum of the lengths of the four sides, we<BR>\n" );
document.write( "can write an equation:<BR>\n" );
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document.write( "P = a + b + c + d<BR>\n" );
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document.write( "in which P represents the perimeter and a, b, c, and d represent the 4 sides. But in<BR>\n" );
document.write( "a square, all the sides are equal in length. Let's call that length \"a\". This makes<BR>\n" );
document.write( "the perimeter equation become:<BR>\n" );
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document.write( "P = a + a + a + a<BR>\n" );
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document.write( "and the four terms on the right side add up to 4a.<BR>\n" );
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document.write( "Therefore, for a square we can say <BR>\n" );
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document.write( "P = 4a <BR>\n" );
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document.write( "where \"a\" is the length of one of the sides. The problem tells you that the perimeter of<BR>\n" );
document.write( "the square is 28 feet. So we can replace P with 28 in the equation to get:<BR>\n" );
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document.write( "28 = 4a<BR>\n" );
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document.write( "Finally, we can solve for \"a\" (which is the length of one side) by dividing both sides of<BR>\n" );
document.write( "this equation by 4. This division will make the right side of the equation become just<BR>\n" );
document.write( "\"a\" and the left side of this equation will be 28/4 which is 7. So the equation reduces to:<BR>\n" );
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document.write( "7 = a<BR>\n" );
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document.write( "And that is the answer. The length of any side of the square is 7 feet.<BR>\n" );
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document.write( "Now on to the second problem. This problem involves a triangle. And we know that a triangle has <BR>\n" );
document.write( "three sides. A triangle can have all sides equal, two sides equal, or no sides equal. In <BR>\n" );
document.write( "this problem the sides are described as shortest, medium, and longest. So we have a <BR>\n" );
document.write( "triangle with all sides different in length.  Since we know that the triangle has 3 sides<BR>\n" );
document.write( "and all sides are different we can write the perimeter equation as:<BR>\n" );
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document.write( "P = a + b + c<BR>\n" );
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document.write( "where P is the perimeter and a, b, and c are the different lengths of the 3 sides.<BR>\n" );
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document.write( "Now let's look at the information in the problem about the three sides. Let's call the<BR>\n" );
document.write( "shortest side \"a\". Then note that the other sides (b and c) are expressed in terms of<BR>\n" );
document.write( "\"a\". The medium side (call it side b) is 3 inches longer than \"a\". So side b is equal to a + 3.<BR>\n" );
document.write( "Then we are told that the longest side (side c) is twice as long as the shortest side \"a\". So<BR>\n" );
document.write( "we know that c = 2a.<BR>\n" );
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document.write( "Now let's return to the perimeter equation and substitute \"a\" for \"a\", \"a + 3\" for b, and<BR>\n" );
document.write( "2a for c. When we do those substitutions the perimeter equation becomes:<BR>\n" );
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document.write( "P = a + a + 3 + 2a<BR>\n" );
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document.write( "If we add up all the terms on the right side that contain the letter \"a\" the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "P = 4a + 3<BR>\n" );
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document.write( "Now, recall that the problem told us that P was 23 inches. So, let's substitute 23 inches<BR>\n" );
document.write( "for P and get:<BR>\n" );
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document.write( "23 = 4a + 3<BR>\n" );
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document.write( "We need to get rid of the +3 on the right side. Do this by subtracting 3 from both sides<BR>\n" );
document.write( "and this makes the equation become:<BR>\n" );
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document.write( "20 = 4a<BR>\n" );
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document.write( "Solve for \"a\" (the shortest side) by dividing both sides by 4 and you have:<BR>\n" );
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document.write( "5 = a<BR>\n" );
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document.write( "So \"a\" is 5 inches.  The medium side is 3 inches longer than the short side. So the medium<BR>\n" );
document.write( "side is 5 + 3 = 8 inches. And the longest side is twice the length of the shortest side.<BR>\n" );
document.write( "So the longest side is 2 times 5 which equals 10 inches.<BR>\n" );
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document.write( "In summary the three sides are 5, 8, and 10 inches.<BR>\n" );
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document.write( "To check, add these three sides together and you should have the perimeter. Sure enough ...<BR>\n" );
document.write( "5 + 8 + 10 does equal 23 inches, just as the problem said it should.<BR>\n" );
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document.write( "Hope this helps you to understand the problems and how to solve them.  Don't panic about<BR>\n" );
document.write( "this stuff ... stay cool and go back to the basics. You don't even have to say what equation<BR>\n" );
document.write( "should I use ... just use what you already know and try to think your way through the<BR>\n" );
document.write( "problem. That's what math is all about. Eventually, it will get to be second nature to you<BR>\n" );
document.write( "... once you get a lot of practice in. Good luck and keep plugging away at it.<BR>\n" );
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