In triangle prs above, rt is the altitude to side ps and qs is the altitude to side pr. if rt = 7, pr = 8, and qs = 9, what is the length of ps?

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