document.write( "Question 1041012: Q: two line segment in the x y plane form a right triangle with the x axis,Having vertices (2,a),(0,0),(10,0).what is the area of triangle? \n" ); document.write( "

Algebra.Com's Answer #656025 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Q: two line segment in the x y plane form a right triangle with the x axis, having vertices (2,a),(0,0),(10,0).
\n" ); document.write( "What is the area of triangle?
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document.write( "It is clear that the vertex (2,a) is the right angle vertex and the segment [(0,0 - (10,0)] is the hypotenuse.\r\n" );
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document.write( "Then you can write the Pythagorean equation in the form\r\n" );
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document.write( " = .       (1)\r\n" );
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document.write( "It is your equation to find the unknown value of \"a\".\r\n" );
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document.write( "Simplify and solve it:\r\n" );
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document.write( " = ,\r\n" );
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document.write( " = ,\r\n" );
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document.write( " =   --->   =   --->  a = 4.\r\n" );
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document.write( "Now, the hypotenuse has the length 10, while the altitude drawn to the hypotenuse has the length 4.\r\n" );
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document.write( "Hence, the area of the triangle is  = 20 square units.\r\n" );
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document.write( "Answer.  The area of the triangle is 20 square units.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Comment from student: can you tell me how you made this equation.\r
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\n" ); document.write( "\n" ); document.write( "My response:\r
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document.write( "Let A be the point (0,0) in the coordinate plane (the origin);\r\n" );
document.write( "let B be the point (2,a), and let C be the point (10,0).\r\n" );
document.write( "Then the triangle ABC is right-angled triangle, according to the condition.\r\n" );
document.write( "with the vertex B as the right angle and the segment AC as the hypotenuse.\r\n" );
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document.write( "Next, draw the perpendicular from the vertex B to the hypotenuse AC. The foot of this perpendicular is the point D = (2,0).\r\n" );
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document.write( "I recommend you to make a sketch of the triangle ABC and draw this perpendicular CD.\r\n" );
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document.write( "Now you have two right angled triangles, ADB and CDB.\r\n" );
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document.write( "From the triangle ADB you have  = .\r\n" );
document.write( "From the triangle CDB you have  = .\r\n" );
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document.write( "The equation (1) in my very first post is\r\n" );
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document.write( " +  = .\r\n" );
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document.write( "Everything is so obvious . . . \r\n" );
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\n" ); document.write( "\n" ); document.write( "I have a contr-question to you.\r
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\n" ); document.write( "\n" ); document.write( "Why, when sending your question, you didn't mention the ID number of the problem?\r
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