document.write( "Question 276490: A triangle with sides of length 13, 14 and 15 inches is to be cut whole from a rectangular sheet of paper. Expressed in square inches, what is the minimum area that this rectangular sheet can have?\r
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Algebra.Com's Answer #201474 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Let's draw a rectangle in which that triangle is circumscribed:\r\n" );
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document.write( "Let's draw an altitude h of that triangle\r\n" );
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document.write( "Now you can see that the original triangle's area is half of the\r\n" );
document.write( "large rectangle's area because each of the two right triangles w\r\n" );
document.write( "which the altitude divides the original triangle into are congruent \r\n" );
document.write( "to the right triangles above it with which it shares a hypotenuse.\r\n" );
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document.write( "This would be true regardless of which side of the original\r\n" );
document.write( "triangle we chose for a side of the rectangle in which it is\r\n" );
document.write( "inscribed.  So we know that the sheet of paper would have to\r\n" );
document.write( "have twice the area of the triangle.\r\n" );
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document.write( "Since the base of that triangle is 14, we will call the left part of\r\n" );
document.write( "that base x, then the right part of it is 14-x.\r\n" );
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document.write( "Applying the Pythagorean theorem to both right triangles into which \r\n" );
document.write( "the original triangle is split we have this system:\r\n" );
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document.write( "Simplifying the second one:\r\n" );
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document.write( "So our system is now:\r\n" );
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document.write( "and therefore\r\n" );
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document.write( "since things equal to the same thing are equal to each other.\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "And since the height of the rectangle equals\r\n" );
document.write( "the altitude, h, of the triangle, the area\r\n" );
document.write( "of the rectangle in which the original triangle\r\n" );
document.write( "is inscribed is found by \r\n" );
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document.write( "So the correct choice is (a) 168\r\n" );
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document.write( "Edwin

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