A computer program that translates a program statement

In triangle ABC, DE is drawn parallel to BC, meeting AB at D and AC at E. If AD : DB = 3 : 2 and the area of triangle ADE is 45 cm², find:

The inner-radius of a triangle is 5 cm, and the sum of lengths of its sides is 60 cm. What is the area of the triangle (in sq. cm.)?

What is the height of an equilateral triangle if each side measures 8√3 cm?

Find area of a trapezium with parallel sides 12 cm and 18 cm, height 10 cm.

If perpendicular and base of a right-angle triangle is, 24 cm and 32 cm, respectively, then find the length of the shortest median of triangle.

What is the inradius of an equilateral triangle whose vertical height measures 12√3 cm?

Find the altitude of an equilateral triangle whose side is 8√3 cm.

In a triangle with sides 13, 14, and 15 cm, find the height corresponding to the longest side.

In the given figure, AB ∥ QP, AB = x, PQ = x + 10, RB = x/2, BP = x + 1. Find PQ.