If in a triangle of base 'a', the ratio of the other two sides is r ( <1).Show that the altitude of the triangle is less than or equal to `(ar)/(1-r^2)`

The ratio of the area of two similar triangle is 4:5 , the ratio of their corresponding sides are :

The perimeter of a triangle is 8 cm. If one of the sides of the triangle be 3 cm, what will be the other two sides for maximum area of the triangle ?

Each of sides of a triangle is 8cm less than the sum of its other two sides.Area of the triangle ( in cm^(2)) is

Read the statemenst carefully and state 'T' for true and 'F' for false . 1. If a line divides any two sides of a triangle in the same ratio , then the line is parallel to the third side of the triangle . 2 . The internal bisector of an angle of a triangle divides the opposite side inernally in the ratio of the sides containing the angle . 3 . If a line through one vertex of a triangle divides the opposite in the ratio of other two sides , then the line bisects the angle at the vertex . 4.Any line parallel to the parallel sides dividesproportionally . 5. Two times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle .

The ratio of areas of two similar triangles is 4:9. Then, the ratio of their sides is:

The ratio of the areas of two similar triangles is 5:3 , then ratio of their corresponding sides is :

If the base of a triangle and the ratio of the lengths of the other two unequal sides are given,then the vertex lies on