document.write( "Question 1195528: A window has the shape of a square of side length 60 cm surmounted by a segment of a circle of radius 50 cm. The circle segment is less than a semicircle. What is the maximum height, in centimetres, of the window? \n" ); document.write( "

Algebra.Com's Answer #828036 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "A window has the shape of a square of side length 60 cm surmounted
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document.write( "Make a sketch on your own.\r\n" );
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document.write( "In the sketch, the center of the circle is somewhere inside the square.\r\n" );
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document.write( "Connect the center with the square's upper corners by straight lines.\r\n" );
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document.write( "Draw a perpendicular from the center to the mid-point of the upper horizontal\r\n" );
document.write( "side of the square.\r\n" );
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document.write( "In the sketch, you have a right-angled triangle.\r\n" );
document.write( "Its hypotenuse is 50 cm. One of its leg (horizontal) is 60/2 = 30 cm long.\r\n" );
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document.write( "Hence, according to the Pythagorean theorem, its other leg (vertical) has\r\n" );
document.write( "the length of   = 40 cm.\r\n" );
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document.write( "It means that the maximum height of the window is 60 cm + 60 cm + (50-40) cm = 130 cm.\r\n" );
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document.write( "ANSWER.  The maximum height of the window is 130 centimeters.\r\n" );
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