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
Answered by Thomas F. Maths tutor

3248 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do I solve 7x – 8 = -3x + 2?


How do you expand brackets? eg. (2x+3)(3x+4)


How do you factorise a quadratic equation?


An isosceles triangle has a base with length x+4 and the other two sides have length x+3. The perimeter of this isosceles triangle is 16cm. Find the area of the triangle.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning