{
    "isOldForm": false,
    "must_get_html_from_browser": true,
    "subparts": [],
    "configString": " [name(X,\"X\"),rectangle_side_with_var(\"PQRS\",\"PQ\",\"QR\",x,5,-4,17,-4),poly_area(\"PQRS\",15444),config_for_parser([\"rectangle(dimension(8,16),label_1(string(17x - 4)),label_2(string()),label_3(string()),label_4(string(5x - 4)),name(Q,R,S,P))\"]),config_text([\"string(latex(PQRS) is a rectangle such that latex(PQ = (5x - 4))cm and latex(QR = (17x - 4))cm. If the area of the rectangle is latex(15444 cm^2),)\"]),name(P,\"P\")]",
    "questionString": " [rectangle(dimension(8,16),label_1(string(17x - 4)),label_2(string()),label_3(string()),label_4(string(5x - 4)),name(Q,R,S,P)), string(latex(PQRS) is a rectangle such that latex(PQ = (5x - 4))cm and latex(QR = (17x - 4))cm. If the area of the rectangle is latex(15444 cm^2), find the perimeter of latex(PQRS). )]",
    "hintString": " [string(Area = Product of two adjacent sides.),string(If latex(ax^2 + bx + c = 0) then latex( x = \\\\frac{-b \\\\pm \\\\sqrt {b^2 - 4ac} }{2a }).),string(Put the value of latex(x) in the equation of sides.),string(Perimeter = 2 x Summation of two adjacent sides.)]",
    "answerTypeString": " [answer_types([[string(Perimeter = ),type(s_textbox)]])]",
    "solutionString": " [string(Product of adjacent sides = Area),string(latex(\\\\therefore (5x - 4) \\\\times (17x - 4) = 15444)),string(latex(5\\\\times 17 \\\\times x^2 + (5 \\\\times -4  - 4 \\\\times 17) \\\\times x + (-4 \\\\times -4 - 15444) = 0)),string(latex(\\\\therefore 85x^2 - 88x - 15428 = 0)),string(Comparing latex(85x^2 - 88x - 15428 = 0) with latex(ax^2 + bx + c = 0)),string(Thus, latex(a = 85, b = -88, c = -15428)),string(latex(\\\\therefore b^2 - 4ac = (-88)^2 - 4 \\\\times 85 \\\\times -15428 = 5253264)),string(Now, latex(x = \\\\frac{-(-88) \\\\pm \\\\sqrt {5253264} }{2 \\\\times 85}) latex(\\\\text{~~~~}) (Quadratic formula)),string(latex(x = \\\\frac{-(-88) - 2292}{2 \\\\times 85} = -12.964705882352941) or latex(x = \\\\frac{-(-88) + 2292}{2 \\\\times 85} = 14)),string(latex(\\\\therefore) latex(x \\\\approx -12.96) or latex(x = 14)),string(When latex(x = -12.96)),string(latex(PQ = 5x - 4 = 5 \\\\times -12.96 - 4 = -68.8 \\\\leq 0 ) Hence, this side is not possible.),string(latex(QR = 17x - 4 = 17 \\\\times -12.96 - 4 = -224.32 \\\\leq 0 ) Hence, this side is not possible.),string(When latex(x = 14)),string(latex(PQ = 5x - 4 = 5 \\\\times 14 - 4 = 66) cm),string(latex(QR = 17x - 4 = 17 \\\\times 14 - 4 = 234) cm),string(Perimeter of latex(PQRS) = 2 x Summation of two adjacent sides latex( = 2 \\\\times (PQ + QR) = 2 \\\\times (66 + 234) = 600 cm)),]"
}