In triangle ABC DE, the midline. The area of triangle ADE is 39. Find the area of triangle ABC.

Let us prove that triangles ABC and ADE are similar.

By the condition DE – the middle line of the triangle ABC, which means it is parallel to the base of the BC.

The angle A is common for triangles, and the angle ABE = ABC as the corresponding angles at the intersection of parallel straight lines BC and DE secant AB. Then the triangles ADE and ABC are similar in two angles.

Let’s determine the coefficient of their similarity.

The midline of a triangle is half the length of the side parallel to it. K = BC / DE = 2.

The ratio of the areas of such triangles is K ^ 2, then Savc / Sade = 2 ^ 2 = 4.

Savs = 4 * 39 = 156 cm2.

Answer: The area of ​​triangle ABC is 156 cm2.