A scalene triangle PQR, where PQ is (3x+4)m long, QR is (2-x)m long and angle PQR is 30 degrees, has an area of 2 square metres. Find x.
Knowledge of equation Area = 1/2absinC where a = PQ b = QR and C = angle PQR, a diagram may aid with visualisation. (B1)
Substituting in values and expanding. 1/2(3x+4)(2-x)sin(30) = 2 becoming 1/4(-3x^2+2x+8)=2 or simplified -3x^2+2x+8 = 8. (M1)
Rearranging and factorising to solve for x. -3x^2+2x+8 = 8 becoming 3x^2-2x = 0 and factorising to x(3x-2)=0. (M2)
Correct answers, 0m and 2/3m (A1)(A2)
TF
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