document.write( "Question 243265: One base of a trapezoid measures 5 cm. more than the other while the altitude is 4/3 times as long as the shorter base. Find the lenghts of the bases if the area is 100 cm². \n" ); document.write( "

Algebra.Com's Answer #178351 by kamaldas(6) $\"\"$ $\"About$

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Area of a trapezoid = 1/2 *(base1 +base2) * altitude\r
\n" ); document.write( "\n" ); document.write( "Lets assume shorter base = b
\n" ); document.write( "Given:
\n" ); document.write( "Longer base = b+5
\n" ); document.write( "Altitude = 4/3 b
\n" ); document.write( "Area = 100\r
\n" ); document.write( "\n" ); document.write( "Area of a trapezoid = 1/2 *(base1 +base2) * altitude
\n" ); document.write( "100 = 1/2 * (b+b+5) * 4/3 b
\n" ); document.write( "100 = 2/3 * (2 b +5) * b
\n" ); document.write( "Multiplying both sides by 3
\n" ); document.write( "300 = 2 * (2 b +5) * b
\n" ); document.write( "300 = 4b^2 + 10b
\n" ); document.write( "4b^2 +10b -300 =0
\n" ); document.write( "2b^2 +5b -150 =0
\n" ); document.write( "Factoring
\n" ); document.write( "(2b - 15) (b +10)=0
\n" ); document.write( "or b = 15/2 or -10
\n" ); document.write( "As distance is not negative
\n" ); document.write( "b =15/2 or 7.5 cm\r
\n" ); document.write( "\n" ); document.write( "Shorter base = 7.5 cm
\n" ); document.write( "Longer base = 7.5+5 =12.5 cm\r
\n" ); document.write( "\n" ); document.write( "Altitude = 4/3 *7.5 =10 cm \n" ); document.write( "

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