I believe that the problem should read as follows:
In a triangle PQR, angle PQR is a right angle. QS is a line segment drawn on the hypotenuse and perpendicular to the hypotenuse. Line segment PS is 25, line segment RS is 4. What is the area of the triangle PQR?
a. 125
b.145
c. 240
d. 290
e. Cannot be determined
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, the 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/25.
In triangle QRS:
(side opposite x)/(side opposite y) = 4/h.
Since the ratios must be equal:
h/25= 4/h
h² = 4*25
h = 2*5 = 10.
Area of PQR = (1/2)bh = (1/2)(29)(10) = 145.
The correct answer is
B.
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