In similar triangles, the ratio of corresponding altitudes is 2 : 5. What is the ratio of their areas?

In triangle ABC, medians AD, BE, and CF intersect at the centroid G. What is the ratio of the area of triangle GAB to the area of triangle ABC?

In △ABC, a line segment DE is parallel to BC, with D on AB and E on AC. If the ratio of the area of △ADE to the area of the trapezoid DECB is 4 : 21, what is the ratio of AD to DB?

A right triangle has sides 3, 4, and 5. A smaller triangle is drawn inside it with its vertices on the sides of the larger triangle, such that it is similar to the larger triangle. If its perimeter is 6, what is its area?

In a triangle ABC, medians AD and BE intersect at G. If the length of median AD is 12 cm, what is the length of the segment AG?

Two right-angled triangular blocks, ABC and DEF, have ∠B = ∠E = 90°. If the lengths of the hypotenuses AC and DF are equal, and the sides AB and DE are equal, are the triangles congruent? If so, by what rule?

The angle bisectors of triangle ABC converge at the incenter I. Given that the measure of ∠BIC is 125°, what is the measure of ∠BAC?

In triangle ABC, a line segment DE is drawn through the centroid G, parallel to side BC. D lies on AB and E lies on AC. What is the ratio of the area of the smaller triangle ADE to the area of the trapezoid DECB?

A circle is circumscribed about a triangle. If one of the angles of the triangle is 120°, and the radius of the circumscribed circle is r, what is the length of the side opposite the 120° angle?

G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:

If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?

What is the area of quadrilateral ABCD?

It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?