Triangles Test ...

In the given figure, $$\angle$$B = $$90^{\circ}$$, $$XY|| BC$$, $$AB = 12\  cm$$, $$AY = 8\  cm$$ and $$AX : XB = 1 : 2$$. Find the length of $$AC$$ and $$BC$$.

Triangle $$ABC$$ is right -angled at $$C$$. Find $$BC$$, If $$AB = 9 \ cm$$ and $$AC = 1\  cm$$.
In each case, answer correct to two place of decimal. 

Find AE, if BD = 4.1 cm

Find $$DF,$$ if $$CG = 11\ cm$$

Triangle ABC is right -angled at C. Find $$AC, $$ If $$AB = 2.2 \ cm\,\, $$and$$\,\, BC = 1.8 \ cm$$.
In each case, answer correct to two place of decimal.

Find GE, if FE = 4 cm

If the measures of sides of a triangle are $$(x^2-1) \ cm, \ (x^2 +1) \ cm$$, and $$2x \ cm$$, then the triangle will be: 

Two isosceles triangles have equal vertical angles and their areas are in the ratio $$16:25$$. Find the ratio of their corresponding heights.

In figure, $$\angle BAC={90}^{o}$$ and $$AD\bot BC$$. Then

$$E$$ and $$F$$ are respectively, the mid points of the sides $$AB$$ and $$AC$$ of $$\Delta ABC$$ and the area of the quadrilateral $$BEFC$$ is $$k$$ times the area of $$\Delta ABC$$. The value of $$k$$ is :