Sample QuestionsSimilarity questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Given is a triangle with sides $3 \ cm, 5 \ cm$ and $6 \ cm.$ Find the sides of a triangle which is similar to the given triangle and its shortest side is $4.5 \ cm.$
View full solution →A model of a ship is made to a scale of $1:500.$ Find: The length of the ship, if length of the model is $1.2.$
View full solution →A model of cargo tuck is made to a scale of $1:40.$ The length of the model is $15\ cm.$ Calculate: The length of the truck
View full solution →$\triangle ABC$ is enlarged, with a scale factor $5.$ Find $:\text{BC}, \text{B'C'} = 16\ cm$
View full solution →$\triangle ABC$ is enlarged, with a scale factor $5.$ Find $:\text{ A'B'},$ if $\text{AB} = 4\ cm$
View full solution →Two figures are similar. If the ratio of their perimeters is $8:16.$ What will be the ratio of the corresponding sides?
View full solution →On a map drawn to a scale of $1:25000,$ a triangular plot of land is right angled and the sides forming the right angle measure $225\ cm$ and $64\ cm.$ Find: The area of the plot in sq. km.
View full solution →On a map drawn to a scale of $1:25000,$ a triangular plot of land is right angled and the sides forming the right angle measure $225\ cm$ and $64\ cm.$ Find: The actual length of the sides in $km$
View full solution →On a map drawn to a scale of $1:25000,$ a rectangular plot of land has sides $12\ cm \times 16\ cm.$ Calculate: The area of the plot in $sq \ km$
View full solution →On a map drawn to a scale of $1:25000,$ a rectangular plot of land has sides $12\ cm \times 16\ cm.$ Calculate: The diagonal distance of the plot in $km$
View full solution →The areas of two similar triangles are $16\ cm^2$ and $9\ cm^2$ respectively. If the altitude of the smaller triangle is $1.8\ cm$, find the length of the altitude corresponding to the larger triangle.
View full solution →Harmeet is $6$ feet tall and casts a shadow of $3$ feet long. What is the height of a nearby pole if it casts a shadow of $12$ feet long at the same time?
View full solution →A plot of land of area $20 \mathrm{~km}^2$ is represented on the map with a scale factor of $1:200000.$ Find: The ground area in $\mathrm{km}^2$ that is represented by $2 \mathrm{~cm}^2$ on the map.
View full solution →The scale of a map is $1 : 50000.$ The area of a city is $40 sq \ km$ which is to be represented on the map. Find: The area of land represented on the map.
View full solution →On a map drawn to a scale of $1: 2,50,000,$ a triangular plot of land has the following measurements:$AB = 3\ cm, BC = 4\ cm, \angle ABC = 90^\circ.$ Calculate$:(i)$ The actual length of $AB$ in $km.(ii)$ The area of Plot in $sq. \ km.$
View full solution →In $\triangle ABC , DE$ is drawn parallel to $BC$ cutting $AB$ in the ratio $2: 3$. Calculate:$ \text { (i) } \frac{\operatorname{area}(\triangle ADE )}{\operatorname{area}(\triangle ABC )};\text { (i) } \frac{\operatorname{area}(\text {trapezium EDBC})}{\operatorname{area}(\triangle ABC)}$
View full solution →$D$ and $E$ are points on the sides $A B$ and $A C$ of $\triangle A B C$ such that $D E \| B C$ and divides $\triangle A B C$ into two parts, equal in area. Find $\frac{ BD }{ AB }$.
View full solution →The areas of two similar triangles are $169\ cm^2$ and $121\ cm^2$ respectively. If one side of the larger triangle is $26\ cm,$ find the length of the corresponding side of the smaller triangle.
View full solution →In a $\triangle ABC, AB = 4 \ cm, BC = 4.5 \ cm$ and $CA = 5 \ cm$. Construct $\triangle ABC$. Find the image $A\ 'B\ 'C$ of the $\triangle ABC$ obtained by enlarging it by a scale factor $2$. Measure the sides of the image $A 'B\ 'C'$ and show that $AB:A\ 'B\ ' = AC:B\ 'C\ ' = CA:C\ 'A\ '$
View full solution →Find the scale factor in each of the following and state the type of size transformation:Model volume $= 200\ cm^3$, Actual volume $= 8\ cm^3$
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