The Diagram shows the Triangle PQR. PQ = x cm. PR = 2x cm. Angle QP^R = 30 degrees. The area of the triangle PQR = A cm^2. Show that x = (Squared Root){2A

Area of a Triangle Formula is
A = 1/2 abSINc
Label the sides of the triangle PR = 2x = a PQ = x = b
1/2 (x) 2x (x) x (x) SINc = A = x² SINc
Rearrange the equation to give
(squared root) { A = x { SINc
QP^R = 30, thereforeQP^R = SIN(30) = 1/2
A divided by 1/2 = 2A
Therefore x = (squared root){2A