rommysingh wrote:In the diagram to the right, triangle PQR has a right angle at Q and line segment QS is perpendicular to PR. If line segment PS has a length of 16 and line segment SR has a length of 9, what is the area of triangle PQR?
72
96
108
150
200
QS is a height drawn through the right angle of triangle PQR.
A height drawn through the right angle of a triangle forms THREE SIMILAR TRIANGLES.
In the figure above:
The angles of triangle PQS are x-y-90.
The angles of triangle QRS are x-y-90.
The angles of triangle PQR are x-y-90.
Since each triangle has the same combination of angles, all 3 triangles are similar.
Since triangle PQS is similar to triangle QRS, the ratio of the legs in each triangle must be the same.
In triangle PQS:
(side opposite x)/(side opposite y) = h/16.
In triangle QRS:
(side opposite x)/(side opposite y) = 9/h.
Since the ratios must be equal:
h/16 = 9/h
h² = 9*16
h = 3*4 = 12.
Area of PQR = (1/2)bh = (1/2)(12)(25) = 150.
The correct answer is
D.
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