document.write( "Question 1202022: Find valu of 'x' in a trapezium where parallel sides are 50m and 26m respectively. Total area is 1254 sqm . Area 1 of upper portion is 618sqm and area2 of lower portion is 636sqm. Height of whole trapezium is 33m. x is height of lower portion of trapezium. Trapezium is divided by a segment in two unequal portions. \n" ); document.write( "

Algebra.Com's Answer #836667 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Here is a crude sketch based on the given information:

\r\n" );
document.write( "\r\n" );
document.write( "                   26\r\n" );
document.write( "        ************************\r\n" );
document.write( "       *                         *\r\n" );
document.write( "      *                            *\r\n" );
document.write( "     *   A = 618                     *\r\n" );
document.write( "    *                                  *\r\n" );
document.write( "   *************************************** -----------\r\n" );
document.write( "  *                                        *\r\n" );
document.write( " *      A = 636                              * height x\r\n" );
document.write( "************************************************-----\r\n" );
document.write( "                    50\r\n" );
document.write( "

\n" ); document.write( "The area of the trapezoid is 1254, which is (altitude) times (average of bases):

\n" ); document.write( "1254 = h((50+26)/2)
\n" ); document.write( "1254 = 38h
\n" ); document.write( "h = 1254/38 = 33

\n" ); document.write( "Since the height of the lower portion is x, the height of the upper portion is 33-x.

\n" ); document.write( "Since the formula for the area of a trapezoid is (altitude) times (average of bases), for convenience let 2y be the length of the segment parallel to the two bases. We then have this sketch:

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document.write( "\r\n" );
document.write( "                   26\r\n" );
document.write( "        ************************----------------------\r\n" );
document.write( "       *                         *\r\n" );
document.write( "      *                            *\r\n" );
document.write( "     *   A = 618                     *    height 33-x\r\n" );
document.write( "    *                 2y               *\r\n" );
document.write( "   *************************************** -----------\r\n" );
document.write( "  *                                        *\r\n" );
document.write( " *      A = 636                              * height x\r\n" );
document.write( "************************************************-----\r\n" );
document.write( "                    50\r\n" );
document.write( "

\n" ); document.write( "Then for the areas of the two trapezoids we have

\n" ); document.write( " $\"%2833-x%29%28%282y%2B26%29%2F2%29=618\"$ [1]
\n" ); document.write( " $\"x%28%282y%2B50%29%2F2%29=636\"$ [2]

\n" ); document.write( "Simplify [1]

\n" ); document.write( " $\"%2833-x%29%28y%2B13%29=618\"$
\n" ); document.write( " $\"33y%2B429-xy-13x=618\"$
\n" ); document.write( " $\"-xy-13x%2B33y=189\"$ [3]

\n" ); document.write( "Simplify [2]

\n" ); document.write( " $\"x%28y%2B25%29=636\"$
\n" ); document.write( " $\"xy%2B25x=636\"$ [4]

\n" ); document.write( "Add [3] and [4]

\n" ); document.write( " $\"12x%2B33y=825\"$
\n" ); document.write( " $\"4x%2B11y=275\"$ [5]

\n" ); document.write( "Solve [5] for x and substitute in [4]

\n" ); document.write( "I leave the rest to you. The numbers work out to give a very ugly irrational value for x, which leads me to believe that the given numbers are not right....

\n" ); document.write( " \n" ); document.write( "

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