Tag: maths

Questions Related to maths

If one shape becomes another using rotation / reflection, then the shapes are __________.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. similar

  2. congruent

  3. mirror images

  4. none of the above

Show answer
Correct Option: B
Explanation:

If the size of the figure does not get affected by rotation or reflection, then the figure will remain same and it will be congruent.

If the area of square is $36\pi \ \text{cm}^2$. If its length is scaled three times, what would be its new area?

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $342\pi$

  2. $324\pi$

  3. $352\pi$

  4. $322\pi$

Show answer
Correct Option: B
Explanation:

Area of square whose side is $a =a^2$ 

If its length is scaled three times, then area $=9a^2$
Therefore, new area $=9\times 36\pi \text{cm}^2=324\pi \text{cm}^2$

The measure of $3.4\ cm$ on a $2:1$ scaled model will be:

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $3.4\ cm$

  2. $6.8\ cm$

  3. $1.7\ cm$

  4. $4.5\ cm$

Show answer
Correct Option: C
Explanation:

Let orignal length $=l$ and scales length $=sl$

$\dfrac { l }{ sl } =\dfrac { 2 }{ 1 } \ \dfrac { 3.4 }{ sl } =\dfrac { 2 }{ 1 } \ \Rightarrow sl=1.7$
So option $C$ is correct.

A $30-60-90$ degree triangle is scaled $1.5$ times. The new angles of the triangle are:

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $45-45-90$

  2. $30-60-90$

  3. $37-53-90$

  4. $60-60-60$

Show answer
Correct Option: B
Explanation:

When the triangle is scaled $1.5$ times then length of each side become $1.5$ times but the angle remains the same.

So the new angles are $30-60-90$
Option $B$ is correct.

A submarine is scaled down to $\dfrac{1}{100}$ times for making a model. If the length of the submarine in the scaled down model was $100\ cm$, what is the original length of the submarine?

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. $100\ cm$

  2. $500\ m$

  3. $100\ m$

  4. $500\ cm$

Show answer
Correct Option: C
Explanation:
$L = OriginalLength$
$l=ScaledDownLength= 100cm = 1m$

$\cfrac{l}{L}= \cfrac{1}{100}$
$\cfrac{1m}{L} = \cfrac{1}{100}$
$L= 100m$


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.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 10

  2. 8

  3. 6

  4. 12

Show answer
Correct Option: A
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{C'A'}{CA} = 2.5$
Therefore, $\dfrac{C'A'}{4} = 2.5$
$\Rightarrow C'A' = 4 \times 2.5$
$\Rightarrow C'A' = 10$ cm 

A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find OA, if OA'= 6 cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 2 cm

  2. 3 cm

  3. 4 cm

  4. none of the above 

Show answer
Correct Option: A
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{OA'}{OA} = 3$
$\Rightarrow \dfrac{6}{OA} = 3$
$\Rightarrow OA = \dfrac{6}{3}$
$\Rightarrow OA = 2 $ cm

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.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 6.75 cm

  2. 5.75 cm

  3. 6.25 cm

  4. none of the above

Show answer
Correct Option: A
Explanation:

$\triangle LMN$ is reduced to $\triangle L'M'N'$,
Thus, $\dfrac{L'M'}{LM} = 0.8$
$\Rightarrow \dfrac{5.4}{LM} = 0.8$
$\Rightarrow LM = \dfrac{5.4}{0.8}$
$\Rightarrow LM = 6.75$ cm 

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.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 6.4 cm

  2. 4.4 cm

  3. 5.4 cm

  4. none of the above

Show answer
Correct Option: A
Explanation:

$\triangle LMN$ is reduced to $\triangle L'M'N'$,
Thus, $\dfrac{M'N'}{MN} = 0.8$
$\Rightarrow \dfrac{M'N'}{8} = 0.8$
$\Rightarrow M'N' = 0.8 \times 8$
$\Rightarrow M'N' = 6.4 $ cm 

A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find BC. if B'C'= 15 cm.

maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

  1. 6 cm

  2. 5 cm

  3. 7 cm

  4. none of the above

Show answer
Correct Option: B
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{B'C'}{BC} = 3$
$\Rightarrow \dfrac{B'C'}{BC} = 3$
$\Rightarrow BC = \dfrac{15}{3}$
$\Rightarrow BC = 5$ cm