document.write( "Question 244120: The diagonals of a rectangle are 11 cm long and intersect at a 60 degree angle. How do you find the dimensions of the rectangle? \n" ); document.write( "

Algebra.Com's Answer #178754 by Edwin McCravy(20056) $\"\"$ $\"About$

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The diagonals of a rectangle are 11 cm long and intersect at a 60 degree angle. How do you find the dimensions of the rectangle?
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document.write( "Since the diagonals of a rectangle are both equal in length and bisect\r\n" );
document.write( "each other, the line segments AC and BC are equal to half of 11 cm, or\r\n" );
document.write( "5.5 cm each. That makes triangle ABC isosceles, and therefore the base \r\n" );
document.write( "angles are equal and since they have to be 60° each, that means that \r\n" );
document.write( "triangle ABC is not only isosceles but also equilateral.  Therefore \r\n" );
document.write( "side AB is also 5.5 cm. So we have one dimension of the rectangle \r\n" );
document.write( "immediately as 5.5 cm.  To get the other dimension, draw a line from\r\n" );
document.write( "C perpendicular to AB. Label the point D where it touches AB\r\n" );
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document.write( "Since CD bisects AB, AD's length is half of 5.5 cm or 2.75 cm. Also\r\n" );
document.write( "CD is one-half the height of the rectangle. \r\n" );
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document.write( "Now since triangle ACD is a right triangle we can use the Pythagorean\r\n" );
document.write( "theorem to find CD, which is half the height of the rectangle:\r\n" );
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document.write( "So the height of the rectangle is twice CD.  \r\n" );
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document.write( "Therefore the height is 9.526279442 cm.\r\n" );
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document.write( "So the dimensions of the rectangle are 5.5 cm x 9.526 cm.,\r\n" );
document.write( "approximately.\r\n" );
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document.write( "Edwin

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