HELp meh with this question it very hard

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HELp meh with this question it very hard

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Answer:AB = 7 cmStep-by-step explanation:Use the law of cosines to find the side AB:[tex]AB = \sqrt{(x + 3)^2+x^2-2x(x+3)cos (60)} =[/tex] [tex]\sqrt{x^2+6x+9+x^2-x^2-3x} = \sqrt{x^2+3x+9}[/tex]Use the Heron's area formula next:[tex]A = \sqrt{s(s - a)(s-b)(s-c)}[/tex], where s- semi perimeters = 1/2[x + x + 3 + [tex]\sqrt{x^2+3x+9}[/tex]) = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex])s - a = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2x - 6) = 1/2 ([tex]\sqrt{x^2+3x+9 }[/tex] - 3)s - b = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2x) = 1/2 ([tex]\sqrt{x^2+3x+9}[/tex] + 3)s - c = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2[tex]\sqrt{x^2+3x+9}[/tex]) = 1/2 (2x + 3 - [tex]\sqrt{x^2+3x+9}[/tex])Now(s - a)(s - b) = 1/4 [(x²+3x+9) - 9] = 1/4 (x² + 3x)s(s - c) = 1/4 [(2x + 3)² - (x² + 3x + 9)] = 1/4 (3x²+ 9x) = 3/4(x² + 3x)NextA² = 3/16(x² + 3x)(x² + 3x)300 = 3/16(x² + 3x)²1600 = (x² + 3x)²x² + 3x = 40Substitute this into the first equation:[tex]AB = \sqrt{40 + 9} = 7 cm[/tex]

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