Triangles Test ...

In the given figure, $$QA$$ and $$PB$$ are perpendiculars to $$AB.$$ If $$AO=10$$ cm, $$BO=6$$ cm and $$PB=9$$ cm, find $$AQ.$$

The areas of two similar triangles are $$121$$ cm$$^{2}$$ and $$64$$ cm$$^{2}$$, respectively. If the median of the first triangle is $$12.1$$ cm, then the corresponding median of the other is:

Triangles $$ABC$$ and $$DEF$$ are similar. If the length of the perpendicular $$AP$$ from $$A$$ on the opposite side $$BC$$ is $$2$$ cm and the length of the perpendicular $$DQ$$ from $$D$$ on the opposite side $$EF$$ is $$1$$ cm, then what is the area of $$\triangle ABC\: ?$$

If $$\triangle ABC$$ is similar to $$\triangle DEF$$ such that $$BC=3$$ cm, $$EF=4$$ cm and area of $$\triangle ABC=54\: \text{cm}^{2}.$$ Find the area of $$\triangle DEF.$$ (in cm$$^2$$)

$$D$$ and $$E$$ are respectively the points on the sides $$AB$$ and $$AC$$ of a $$\triangle ABC$$ such that $$AB = 12 \text{ cm},$$ $$AD = 8 \text{ cm},$$ $$AE = 12 \text{ cm}$$ and $$AC = 18 \text{ cm}$$, then

In a $$\Delta ABC,\;D\;and\;E$$ are points on the sides $$AB$$ and $$AC$$ respectively such that $$DE\;\parallel\;BC$$. If $$AD=4x-3,\;AE=8x-7,\;BD=3x-1\;and\;CE=5x-3$$, find the value of $$x$$.

In a $$\displaystyle \bigtriangleup ABC $$, AB = AC = 2.5 cm, BC = 4 cm. Find its height from A to the opposite base.

If $$\Delta ABC\sim \Delta DEF$$ such that area of $$\Delta ABC$$ is $$9 cm^2$$ and area of $$\Delta DEF$$ is $$16 cm^2$$ and $$BC=1.8 cm$$, then EF is

$$\displaystyle \angle BAC={ 90 }^{ o }$$, AD is its bisector. If $$\displaystyle DE\bot AC$$, prove that $$\displaystyle DE\times \left( AB+AC \right) =AB\times AC$$

In the figure, $$\displaystyle PQ\parallel BC$$ and AP : PB = 1 : 2. Find $$\displaystyle \frac { ar\left( \Delta APQ \right)  }{ ar\left( \Delta ABC \right)  } $$.