In the given triangle PRS, QS and RT are the altitudes. An altitude of a triangle is a line segment through a vertex and perpendicular to form a right angle with a line containing the base.
Area of triangle with an altitude = \frac{1}{2}\times base \times height
Area of the triangle with base PR and altitude QS = \frac{1}{2}\times PR \times QS
= \frac{1}{2}\times 8 \times 9 = \frac{72}{2}.
Area of the triangle with base PS and altitude RT = \frac{1}{2}\times PS \times RT
= \frac{1}{2}\times PS \times 7 = \frac{7PS}{2}.
by equating both the areas, we get,
\frac{72}{2}=\frac{7PS}{2}
PS=\frac{72}{7}= 10.3