The lengths of the diagonals of a rhombus are $16 cm$ and $12 cm$. The length of the side of the rhombus is

If a side of a rhombus is $10 cm$ and one of the diagonals is $16 cm$, then the length of the other diagonal is

If a ladder $10 m$ long reaches a window $8 m$ above the ground, then the distance of the foot of the ladder from the base of the wall is

A girl walks $200 \mathrm{m}$ towards East and then she walks $150 \mathrm{m}$ towards North. The distance of the girl from the starting point is 

A ladder reaches a window $12 m$ above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window $9 m$ high. If the length of the ladder is $15 m$, then the width of the street is

In the adjoining figure, line segment $DF$ intersect the side $AC$ of triangle $ABC$ at the point $E$ such that $E$ is mid-point of $CA$ and $\angle AEF=\angle AFE$. Prove that $\frac{BD}{CD}=\frac{BF}{CE}$.

In the adjoining figure, $ABC$ is a triangle right-angled at $B$ and $BD\perp AC.$ If $AD=4 cm$ and $CD=5 cm$, find $BD$ and $AB.$

In the adjoining figure, $ABC$ is an isosceles triangle with $AB=AC=13 cm$ and $BC=10cm$. If $EFGH$ is a square inscribed in $△ABC$, find the area of the shaded region.