Question 1

Two similar triangles have corresponding sides $3$ cm and $5$ cm. The ratio of their areas is:

Accepted Answer

**Answer: (a) $9:25$.** Ratio of areas $=\left(\dfrac{3}{5}\right)^2=\dfrac{9}{25}.$

Question 2

If $	riangle ABC\sim	riangle PQR$ with $\dfrac{AB}{PQ}=\dfrac{2}{3}$, then $\dfrac{	ext{area}(	riangle ABC)}{	ext{area}(	riangle PQR)}$ is:

Accepted Answer

**Answer: (a) $	frac49$.** The area ratio is the square of the side ratio: $\left(\dfrac23ight)^2=\dfrac49.$

Question 3

A model of a building is made to a scale $1:50$. If the model is $40$ cm tall, the actual height of the building is:

Accepted Answer

**Answer: (a) $20$ m.** Actual height $=40	imes50=2000$ cm $=20$ m.

Question 4

The areas of two similar triangles are $81	ext{ cm}^2$ and $49	ext{ cm}^2$. The ratio of their corresponding sides is:

Accepted Answer

**Answer: (a) $9:7$.** Side ratio $=\sqrt{\dfrac{81}{49}}=\dfrac{9}{7}.$

Question 5

**Assertion (A):** In two similar triangles, the ratio of areas equals the ratio of the squares of corresponding sides. **Reason (R):** All congruent triangles are similar.

Accepted Answer

**Answer: (b)** A is a true theorem, and R is also true (congruent triangles are similar with ratio $1:1$), but R does not explain the area result in A.

Question 6

The scale of a map is $1:20000$. Find the actual distance represented by $3$ cm on the map.

Accepted Answer

Actual distance $=3	imes20000=60000$ cm $=600$ m $=0.6$ km.

Question 7

The areas of two similar triangles are $16	ext{ cm}^2$ and $25	ext{ cm}^2$. If a side of the smaller triangle is $4$ cm, find the corresponding side of the larger triangle.

Accepted Answer

Ratio of sides $=\sqrt{\dfrac{16}{25}}=\dfrac{4}{5}.$ If $4$ cm corresponds to $x$: $\dfrac{4}{x}=\dfrac{4}{5}\Rightarrow x=5$ cm.

Question 8

In $	riangle ABC$, $D$ and $E$ lie on $AB$ and $AC$ with $DE\parallel BC$. Given $AD=4$ cm, $DB=6$ cm and $BC=15$ cm, find $DE$.

Accepted Answer

Since $DE\parallel BC$, $ riangle ADE\sim riangle ABC$ (AA). $AB=AD+DB=4+6=10$ cm, so $\dfrac{AD}{AB}=\dfrac{4}{10}=\dfrac25.$ $\dfrac{DE}{BC}=\dfrac{AD}{AB}\Rightarrow DE=15 imes\dfrac25=6$ cm. ```svg ```

Question 9

$	riangle ABC\sim	riangle DEF$ with $BC=4$ cm and $EF=6$ cm. If the area of $	riangle ABC$ is $32	ext{ cm}^2$, find the area of $	riangle DEF$.

Accepted Answer

$\dfrac{	ext{area }ABC}{	ext{area }DEF}=\left(\dfrac{BC}{EF}ight)^2=\left(\dfrac{4}{6}ight)^2=\dfrac{16}{36}=\dfrac49.$ $\dfrac{32}{	ext{area }DEF}=\dfrac49\Rightarrow 	ext{area }DEF=32	imes\dfrac94=72	ext{ cm}^2.$

Question 10

A model of a ship is built to a scale $1:100$. (i) If the actual ship is $300$ m long, find the length of the model. (ii) If the deck of the model has area $0.5	ext{ m}^2$, find the actual deck area. (iii) If the actual ship has volume $6000	ext{ m}^3$, find the volume of the model.

Accepted Answer

Scale factor $k=\dfrac{1}{100}.$

(i) Length: $300\times\dfrac1{100}=3$ m.

(ii) Area scales as $k^2$ : actual $=0.5\div\left(\dfrac1{100}\right)^2=0.5\times100^{2}=5000\text{ m}^2.$

(iii) Volume scales as $k^3$ : model $=6000\times\left(\dfrac1{100}\right)^3=\dfrac{6000}{10^{6}}=0.006\text{ m}^3.$

Question 11

In $	riangle ABC$, $P$ lies on $AB$ and $Q$ on $AC$ with $PQ\parallel BC$. Given $AP=2.4$ cm, $AQ=2$ cm, $QC=3$ cm and $BC=6$ cm, find (i) $PB$, (ii) $AB$, and (iii) $PQ$.

Accepted Answer

Since $PQ\parallel BC$, by the Basic Proportionality Theorem $\dfrac{AP}{PB}=\dfrac{AQ}{QC}.$ (i) $\dfrac{2.4}{PB}=\dfrac{2}{3}\Rightarrow PB=\dfrac{2.4 imes3}{2}=3.6$ cm. (ii) $AB=AP+PB=2.4+3.6=6$ cm. (iii) $ riangle APQ\sim riangle ABC$, so $\dfrac{PQ}{BC}=\dfrac{AQ}{AC}=\dfrac{2}{2+3}=\dfrac25\Rightarrow PQ=6 imes\dfrac25=2.4$ cm. ```svg ```

Question 12

A map is drawn to a scale of $1:50000$. (i) Two towns are $4$ cm apart on the map; find the actual distance between them in km. (ii) A lake covers $8	ext{ cm}^2$ on the map; find its actual area in $	ext{km}^2$. (iii) A forest of actual area $20	ext{ km}^2$ is to be shown; find the area it covers on the map.

Accepted Answer

On the map $1$ cm represents $50000$ cm $=0.5$ km.

(i) Distance $=4\times0.5=2$ km.

(ii) Since $1$ cm represents $0.5$ km, $1\text{ cm}^2$ represents $(0.5)^2=0.25\text{ km}^2.$ So $8\text{ cm}^2\to8\times0.25=2\text{ km}^2.$

(iii) Map area $=\dfrac{20}{0.25}=80\text{ cm}^2.$

Question 13

At the same time of day, a vertical pole $6$ m high casts a shadow $4$ m long, while a nearby tower casts a shadow $28$ m long.

(i) Why is the triangle formed by the pole and its shadow similar to that formed by the tower and its shadow?

(ii) Find the height of the tower.

(iii) At the same time, another pole casts a shadow $10$ m long; find its height.

Accepted Answer

(i) The sun's rays are parallel, so the angles of elevation are equal; both triangles are right-angled at the ground, so they are similar by the AA criterion.

(ii) The ratio $\dfrac{\text{height}}{\text{shadow}}$ is the same: $\dfrac{6}{4}=\dfrac{h}{28}\Rightarrow h=\dfrac{6\times28}{4}=42$ m.

(iii) $\dfrac{6}{4}=\dfrac{H}{10}\Rightarrow H=\dfrac{6\times10}{4}=15$ m.

Question 14

Are these Similarity (With Applications to Maps and Models) important questions free?

Accepted Answer

Yes. All 13 ICSE Class 10 Maths important questions for Similarity (With Applications to Maps and Models) are free, with full model answers and no login required.

Question 15

Do these Similarity (With Applications to Maps and Models) questions follow the latest ICSE syllabus?

Accepted Answer

Yes — they are aligned to the CISCE latest syllabus syllabus for ICSE Class 10 Maths, so nothing here is outside the current course.

Question 16

How should I practise the Similarity (With Applications to Maps and Models) important questions?

Accepted Answer

Attempt each question on paper first, then reveal the model answer to check your method — not just the final result. Re-do anything you got wrong the same day.

Question 17

What types of questions are covered for Similarity (With Applications to Maps and Models)?

Accepted Answer

A full mix — multiple-choice questions, assertion–reason questions, very short answer questions, short answer questions, long answer questions, case-based questions — so every format in the ICSE paper is covered.

Question type	Count	Marks
MCQ	4	1
Assertion–Reason	1	1
Very Short	2	2
Short Answer	3	3
Long Answer	2	5
Case-based	1	4

Similarity (With Applications to Maps and Models) — Important Questions

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Important questions with answers

Multiple-choice questions (1 mark)

Assertion–Reason questions (1 mark)

Very short answer questions (2 marks)

Short answer questions (3 marks)

Long answer questions (5 marks)

Case-based questions (4 marks)

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