One side of a triangle is 18 centimeters. Inside the triangle, a segment is drawn parallel to the 18-cm side.

Question

One side of a triangle is 18 centimeters. Inside the triangle, a segment is drawn parallel to the 18-cm side. Forming a trapezoid whose area is one-third that of the original triangle, find the length of this segment (in cm).

Answer 1

Trapezoid is 1/3 area; the triangle is 2/3 area of original triangle. This smaller triangle is similar to the larger triangle. Use  Area of small triangle/ Area of large triangle = segment ^2/ 18^2.

Solve.

Answer 14.7 cm

Answer 2

A segment parallel to the base cuts the triangle into both a trapezoid and a smaller triangle, which you can show is similar to the original triangle (AAA). Try to solve the problem using the similarity between the two triangles...