JSON -
{
    "isOldForm": false,
    "must_get_html_from_browser": true,
    "subparts": [],
    "configString": " [name(X,\"X\"),trapezium_side_with_var(\"ABCD\",\"AD\",\"BC\",\"AB\",x,4,-56,9,-140,7,-94),poly_area(\"ABCD\",608),config_for_parser([\"trapezium(dimension(5,19,9),labels(string(9x - 140),string(),string(4x - 56),string(7x - 94)),perpendicular(true),name(B,C,D,A))\"]),config_text([\"string(latex(ABCD) is a trapezium in which latex(AD) is parallel to latex(BC), latex(AD = (4x - 56))cm, latex(BC = (9x - 140))cm, latex(AB = (7x - 94))cm, latex(\\\\\\\\angle {ABC} = 90^{\\\\\\\\circ}). If the area of the trapezium is latex(608 cm^2),)\"]),name(A,\"A\")]",
    "questionString": " [trapezium(dimension(5,19,9),labels(string(9x - 140),string(),string(4x - 56),string(7x - 94)),perpendicular(true),name(B,C,D,A)), string(latex(ABCD) is a trapezium in which latex(AD) is parallel to latex(BC), latex(AD = (4x - 56))cm, latex(BC = (9x - 140))cm, latex(AB = (7x - 94))cm, latex(\\\\angle {ABC} = 90^{\\\\circ}). If the area of the trapezium is latex(608 cm^2), find the value of latex(AD), latex(BC) and latex(AB). Give your answers correct to two decimal places.)]",
    "hintString": " [string(Area = latex(\\\\frac{1}{2} \\\\times) Summation of parallel sides x height.),string(If latex(ax^2 + bx + c = 0) then latex( x = \\\\frac{-b \\\\pm \\\\sqrt {b^2 - 4ac} }{2a }).),string(Put the value of x in the equations of sides and height.)]",
    "answerTypeString": " [answer_types([,[string(AD = ),type(s_textbox)],[string(and)],[string(BC = ),type(s_textbox)],[string(and)],[string(AB = ),type(s_textbox)]])]",
    "solutionString": " [string(latex(\\\\angle {ABC} = 90^{\\\\\\\\circ} \\\\therefore AB) is the hieght of trapezium latex(ABCD)),string(latex(\\\\frac{1}{2} \\\\times) Summation of parallel sides x height = Area),string(latex(\\\\therefore \\\\frac{1}{2} \\\\times (AD + BC) \\\\times AB = 608)),string(latex(((4x - 56) + (9x - 140)) \\\\times (7x - 94) = 2 \\\\times 608)),string(latex((13x - 196) \\\\times (7x - 94) = 2 \\\\times 608)),string(latex(13 \\\\times 7 \\\\times x^2 + (13 \\\\times -94  - 196 \\\\times 7) \\\\times x + (-196 \\\\times -94 - 2 \\\\times 608) = 0)),,string(latex(\\\\therefore 91x^2 - 2594x + 17208 = 0)),string(Comparing latex(91x^2 - 2594x + 17208 = 0) with latex(ax^2 + bx + c = 0)),string(Thus, latex(a = 91, b = -2594, c = 17208)),string(latex(\\\\therefore b^2 - 4ac = (-2594)^2 - 4 \\\\times 91 \\\\times 17208 = 465124)),string(Now, latex(x = \\\\frac{-(-2594) \\\\pm \\\\sqrt {465124} }{2 \\\\times 91}) latex(\\\\text{~~~~}) (Quadratic formula)),string(latex(x = \\\\frac{-(-2594) - 682}{2 \\\\times 91} = 10.505494505494505) or latex(x = \\\\frac{-(-2594) + 682}{2 \\\\times 91} = 18)),string(latex(\\\\therefore) latex(x \\\\approx 10.51) or latex(x = 18)),string(When latex(x = 10.51)),string(latex(AD = 4x - 56 = 4 \\\\times 10.51 - 56 = -13.96 \\\\leq 0 ) Hence, this side is not possible.),string(latex(BC = 9x - 140 = 9 \\\\times 10.51 - 140 = -45.41 \\\\leq 0 ) Hence, this side is not possible.),string(latex(AB = 7x - 94 = 7 \\\\times 10.51 - 94 = -20.43 \\\\leq 0 ) Hence, this side is not possible.),string(When latex(x = 18)),string(latex(AD = 4x - 56 = 4 \\\\times 18 - 56 = 16) cm),string(latex(BC = 9x - 140 = 9 \\\\times 18 - 140 = 22) cm),string(latex(AB = 7x - 94 = 7 \\\\times 18 - 94 = 32) cm),]"
}