Question

In triangle PQR, PS is perpendicular to QR and S divides QR in the ratio of $3 : 1$ internally. If $PQ = 21$ and $PR = 9$, find QR.

Accepted Answer

D. Let $SR = x$, then $QS = 3x$. So $QR = 4x$. In $	riangle PSR$: $PS^2 = PR^2 - SR^2 = 9^2 - x^2 = 81 - x^2$. In $	riangle PSQ$: $PS^2 = PQ^2 - QS^2 = 21^2 - (3x)^2 = 441 - 9x^2$. Equating: $81 - x^2 = 441 - 9x^2 \implies 8x^2 = 360 \implies x^2 = 45 \implies x = 3\sqrt{5}$. $QR = 4x = 4(3\sqrt{5}) = 12\sqrt{5}$.

Perpendicular in Triangle

Explanation

Practise this under exam conditions