Triangle Trouble

Geometry Level 2

In fig. angle PQR =60° and ray QT bisects angle PQR . Seg BA is perpendicular to ray QP and seg BC is perpendicular to ray QR. If BC= 8 find perimeter of quadrilateral ABCQ

root 3 16+16 * root 3 12 17* root 3

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1 solution

Marta Reece
Jun 15, 2017

tan 3 0 = 8 Q C \tan30^\circ=\dfrac {8}{QC}

Q C = 8 tan 3 0 = 8 3 QC=\dfrac{8}{\tan30^\circ}=8\sqrt3

A Q + Q C + C B + B A = 8 3 + 8 3 + 8 + 8 = 16 + 16 3 AQ+QC+CB+BA=8\sqrt3+8\sqrt3+8+8=\boxed{16+16\sqrt3}

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