document.write( "Question 1100997: In a rectangle co-ordinate system with a scale of 1 cm= 1 unit on each axis, we have A (0,8), B (6,0) and C (x,12). If x is larger than 0 but smaller than 6 and the area of ABC is 20cm^2, find the value of x. \n" ); document.write( "

Algebra.Com's Answer #715567 by greenestamps(13200) $\"\"$ $\"About$

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Add points D(0,12) and E(6,12) to the diagram, and call the origin point O.

\n" ); document.write( "The area of triangle ABC is the area of rectangle OBED, minus the areas of the three right triangles AOB, BEC, and CDA.

\n" ); document.write( "The area of rectangle OBED is 6*12 = 72.
\n" ); document.write( "The area of triangle AOB is 6*8/2 = 24.
\n" ); document.write( "The area of triangle BEC is 12(6-x)/2 = 36-6x.
\n" ); document.write( "The area of triangle CDA is 4*x/2 = 2x.

\n" ); document.write( "The area of triangle ABC is $\"72+-+24+-+%2836-6x%29+-+2x+=+12%2B4x\"$
\n" ); document.write( "Since the area is supposed to be 20,
\n" ); document.write( " $\"12%2B4x+=+20\"$
\n" ); document.write( " $\"4x+=+8\"$
\n" ); document.write( " $\"x+=+2\"$

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