# In a rectangular trapezoid, the base and the smaller side are equal to a, b, and c, respectively.

In a rectangular trapezoid, the base and the smaller side are equal to a, b, and c, respectively. Find the distances from the intersection of the diagonals to the bases and the smaller side.

Let OK = X cm, OM = Y cm, OH = Z cm.

Rectangular triangles ABD and OKD are similar in acute angle ADB.

Then x / c = (b – y) / b (1).

Right-angled triangles ABC and AMO are similar in acute angle BAC.

Then y / a = x / c (2).

Let’s solve equations 1 and 2 with two unknowns.

y / a = (b – y) / b.

y * b = a * b – a * y.

y * (b + a) = a * b.

y = a * b / (b + a).

Then:

(a * b / (b + a)) / a = x / c.

x * a = c * a * b / (b + a).

x = b * c / (b + a).

Then Z = AB – OK = c – x = c – (b * c / (b + a)).

Answer: The distance to the side is a * b / (b + a), to the larger base b * c / (b + a), to the smaller base (c – (b * c / (b + a))). One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.