Chapter 15 - Similarity (With Applications to Maps and Models) Exercise Ex. 15(D)

Question 1(i)

A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A' B' C' Calculate :

the length of AB, if A' B' = 6 cm. 

Solution 1(i)

 

Question 1(ii)

A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A' B' C' Calculate :

the length of C' A' if CA = 4 cm. 

Solution 1(ii)

 

Question 2(i)

A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate:

the length of M' N', if MN = 8 cm.

Solution 2(i)

 

Question 2(ii)

A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate:

the length of LM, if L' M' = 5.4 cm.

Solution 2(ii)

 

Question 3(iv)

A triangle ABC is enlarged, about the point 0 as centre of enlargement, and the scale factor is 3. Find : OC', if OC = 21 cm

Also, state the value of : 

(a)  

(b)  

Solution 3(iv)

Given that triangle ABC is enlarged and the scale factor is m = 3 to the triangle A'B'C'.

OC = 21 cm

So, (OC)3 = OC'

i.e. 21 x 3 = OC'

i.e. OC' = 63 cm

 

Question 3(i)

A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find :

A' B', if AB = 4 cm.

Solution 3(i)

 

Question 3(ii)

A triangle ABC is enlarged, about the point 0 as centre of enlargement, and the scale factor is 3. Find :

BC, if B' C' = 15 cm. 

Solution 3(ii)

 

Question 3(iii)

A triangle ABC is enlarged, about the point 0 as centre of enlargement, and the scale factor is 3. Find :

OA, if OA' = 6 cm. 

Solution 3(iii)

 

Question 4(i)

A model of an aeroplane is made to a scale of 1 : 400. Calculate :

the length, in cm, of the model; if the length of the aeroplane is 40 m. 

Solution 4(i)

 

Question 4(ii)

A model of an aeroplane is made to a scale of 1 : 400. Calculate :

the length, in m, of the aeroplane, if length of its model is 16 cm.

Solution 4(ii)

 

Question 5

The dimensions of the model of a multistorey building are 1.2 m x 75 cm x 2 m. If the scale factor is 1 : 30; find the actual dimensions of the building.

Solution 5

 

Question 6(i)

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 and  ∠ABC = 90°.

Calculate :

the actual lengths of AB and BC in km. 

Solution 6(i)

 

Question 6(ii)

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 and angle ABC = 90°.

Calculate :

the area of the plot in sq. km.

Solution 6(ii)

 

Question 7

A model of a ship is made to a scale 1 : 300.

 i. The length of the model of the ship is 2 m. Calculate the length of the ship.

 ii. The area of the deck of the ship is 180,000 m². Calculate the area of the deck of the model.

 iii. The volume of the model is 6.5 m³. Calculate the volume of the ship. 

Solution 7