Question 12

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.

Solution

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we have :

Triangles PSR and PSQ are right triangles 
so using pythaghoras theorem
we get
441 = $$PS^2+9x^2$$
81 =$$PS^2+x^2$$
subtracting we get
360=$$8x^2$$
$$x^2\ =45$$
x=$$3\sqrt{\ 5}$$
QR = 4x = $$12\sqrt{\ 5}$$

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