document.write( "Question 198597: Solving Problems with Quadratic Equations
\n" ); document.write( "21. An open-topped box is to be made from a rectangular piece of tin measuring 50 cm by 40 cm by cutting squares of equal size from each corner. The base area is to be 875 cm^2.
\n" ); document.write( "a) Draw a diagram representing the information.
\n" ); document.write( "b) What is the side length of the squares being removed?
\n" ); document.write( "c) What is the volume of the box?
\n" ); document.write( "Thanks1!! \n" ); document.write( "

Algebra.Com's Answer #149143 by josmiceli(19441) $\"\"$ $\"About$

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$\"50%2A40+=+2000\"$ cm2
\n" ); document.write( "Let the edge of the corner squares = $\"x\"$
\n" ); document.write( "After the squares in each corner are cut, the area left is
\n" ); document.write( " $\"2000+-+4x\"$
\n" ); document.write( "The areas of the sides of the box will be
\n" ); document.write( " $\"x%2A%2850+-+2x%29\"$ (times 2) and
\n" ); document.write( " $\"x%2A%2840+-+2x%29\"$ (times 2)
\n" ); document.write( "What is left is the base, so
\n" ); document.write( " $\"2000+-+4x%5E2+=+2x%2A%2850+-+2x%29+%2B+2x%2A%2840+-+2x%29+%2B+875\"$ cm2
\n" ); document.write( " $\"2000+-+4x%5E2+=+100x+-+4x%5E2+%2B+80x+-+4x%5E2+%2B+875\"$
\n" ); document.write( " $\"4x%5E2+-+180x+%2B+1125+=+0\"$
\n" ); document.write( "Use quadratic equation
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+4\"$
\n" ); document.write( " $\"b+=+-180\"$
\n" ); document.write( " $\"c+=+1125\"$
\n" ); document.write( " $\"x+=+%28-%28-180%29+%2B-+sqrt%28+%28-180%29%5E2-4%2A4%2A1125+%29%29%2F%282%2A4%29+\"$
\n" ); document.write( " $\"x+=+%28+180+%2B-+sqrt%28+32400+-+18000+%29%29%2F8+\"$
\n" ); document.write( " $\"x+=+%28+180+%2B-+sqrt%28+14400+%29%29%2F8+\"$
\n" ); document.write( " $\"x+=+%28+180+%2B-+120%29%2F8+\"$
\n" ); document.write( " $\"x+=+60%2F8\"$
\n" ); document.write( " $\"x+=+7.5\"$ cm
\n" ); document.write( "and
\n" ); document.write( " $\"x+=+300%2F8\"$
\n" ); document.write( " $\"x+=+37.5\"$ cm (this is impossible- it's too long)
\n" ); document.write( "The side length of a square is 7.5 cm
\n" ); document.write( "check answer:
\n" ); document.write( " $\"2000+-+4x%5E2+=+2x%2A%2850+-+2x%29+%2B+2x%2A%2840+-+2x%29+%2B+875\"$ cm2
\n" ); document.write( " $\"2000+-+4%2A7.5%5E2+=+2%2A7.5%2A%2850+-+2%2A7.5%29+%2B+2%2A7.5%2A%2840+-+2%2A7.5%29+%2B+875\"$
\n" ); document.write( " $\"2000+-+4%2A56.25+=+15%2A%2850+-+15%29+%2B+15%2A%2840+-+15%29+%2B+875\"$
\n" ); document.write( " $\"2000+-+225+=+15%2A35+%2B+15%2A25+%2B+875\"$
\n" ); document.write( " $\"1775+=+525+%2B+375+%2B+875\"$
\n" ); document.write( " $\"1775+=+1775\"$
\n" ); document.write( "OK
\n" ); document.write( "The volume of the box would be:
\n" ); document.write( " $\"x%2A%2850+-+2x%29%2A%2840+-+2x%29\"$
\n" ); document.write( " $\"7.5%2A%2850+-+15%29%2A%2840+-+15%29\"$
\n" ); document.write( " $\"7.5%2A35%2A25\"$
\n" ); document.write( " $\"6562.5\"$ cm3
\n" ); document.write( "The volume is 6562.5 cm3
\n" ); document.write( "check:
\n" ); document.write( "Volume is also
\n" ); document.write( " $\"875%2Ax\"$
\n" ); document.write( " $\"875%2A7.5+=+6562.5\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );