M L Aggarwal Solutions for Exercise 3: Exercise 13.3

In the figure given below, $DE\parallel BC$ and the ratio of the areas of $△ADE$ and trapezium is $4 :5$. Find the ratio of $DE : BC$.

In the figure given below, $ABCD$ is a trapezium in which$DC$ is parallel to $AB$. If $\mathrm{AB}=9 \mathrm{cm}, \mathrm{DC}=6 \mathrm{cm}$  and $\mathrm{BD}=12 \mathrm{cm}$, find $BP$.

In the figure given below, $ABCD$ is a trapezium in which$DC$ is parallel to $AB$. If $\mathrm{AB}=9 \mathrm{cm}, \mathrm{DC}=6 \mathrm{cm}$  and $\mathrm{BD}=12 \mathrm{cm}$, find the ratio of areas of $△APB$ and $△DPC$.

Two isosceles triangles have equal vertical angles and their areas are in the ratio $7: 16$. Find the ratio of their corresponding height.

On a map drawn to a scale of $1 : 250000$, a triangular plot of land has the following measurements :$\mathrm{AB} = 3 \mathrm{cm}, \mathrm{BC} = 4 \mathrm{cm}$ and $\angle ABC = 90°$. Calculate the actual length of $AB$ in $\mathrm{km}$.

A map of a square plot of land is drawn to a scale $1 :25000$. If the area of the plot in the map is $72 {\mathrm{cm}}^3$. Find actual area of the plot of land.

A map of a square plot of land is drawn to a scale $1 :25000$. If the area of the plot in the map is $72 {\mathrm{cm}}^3$. Find the length of the diagonal in the actual plot of land.

The model of a building is constructed with the scale factor $1: 30$. If the height of the model is $80 \mathrm{cm},$ find the actual height of the building in metres.