Tag: maths

Questions Related to maths

A has a pair of triangles with corresponding sides proportional, and B has a pair of pentagons with corresponding sides proportional.
$S _1 \equiv $ A's triangles must be similar
$S _2 \equiv $ B's pentagons must be similar 
Which of the following statement is correct ? 

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

  1. $S _1$ is true, but $S _2$ is not true.

  2. $S _2$ is true, but $S _1$ is not true.

  3. Both $S _1$ and $S _2$ are true

  4. Neither $S _1$ and $S _2$ are true

Show answer
Correct Option: A
Explanation:

For similarity of triangles we have SSS criteria. So $S _1$ is true. 
But for polygons to be similar, the corresponding sides must be in equal ratio as well as the corresponding angles must be congruent.

Since, there is nothing mentioned about the angles of the pentagons, so $S _2$ is false.

A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find A'B', if AB = 4cm.

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

  1. 12 cm

  2. 14 cm

  3. 22 cm

  4. none of the above

Show answer
Correct Option: A
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{A'B'}{AB} = 3$
$\Rightarrow \dfrac{A'B'}{4} = 3$
$\rightarrow A'B' = 4 \times 3$
$\Rightarrow A'B' = 12 $ cm 

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

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

  1. 63 cm

  2. 53 cm

  3. 43 cm

  4. none of the above

Show answer
Correct Option: A
Explanation:

$\triangle ABC$ is enlarged to $\triangle A'B'C'$,
Thus, $\dfrac{OC'}{OC} = 3$
$\Rightarrow \dfrac{OC'}{21} = 3$
$\Rightarrow OC' = 21 \times 3$
$\Rightarrow OC' = 63 $ cm

A flagstaff $17.5$ m high casts a shaded length of $40.25$ m. The height of the building which costs a shadow of length $28.75$ m under similar conditions will be:

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

  1. $10$ m

  2. $12.5$ m

  3. $17.5$ m

  4. $21.25$ m

Show answer
Correct Option: B
Explanation:

Flagstaff and shade forms right triangle with height $17.5$ m and base $40.25$ m

$\dfrac{17.5}{40.25} = \tan(\theta)$
under similar conditions $\theta$ will remain same.
Lets assume height of the building as $H$
Hence, $ \tan(\theta)=\dfrac{17.5}{40.25}$ $ = \dfrac {H}{20.75}$
$\Rightarrow  H= 12.5$ m

The ratio of the lengths of the corresponding sides of $2$ similar right angled triangles is $2:5$. If the length of the hypotenuse of the smaller triangle is $5$ inches, find the length of the hypotenuse of the larger triangle (in inches):

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

  1. 2

  2. 2.5

  3. 7

  4. 10

  5. 12.5

Show answer
Correct Option: E
Explanation:

Ratio of the length of the sides of the two triangle $=2:5$

If hypotenuse  of small triangle $=5$ inches
Let the hypotenuse of  larger triangle $=x$
$\therefore \dfrac{5}{x}=\dfrac{2}{5}$
$\therefore  x=\dfrac{25}{2}=12.5$  inches

If the image of an object is enlarged, then what would be the effect on scale factor, $k?$

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

  1. $k$ will remain same for both.

  2. $k>1$ for enlarged image.

  3. $k<1$ for enlarged image.

  4. none of the above

Show answer
Correct Option: B
Explanation:


If image is enlarged, $k>1.$
If image size does not change, then $k=1.$
If image size is reduced, $k<1.$

The difference between the place value and face value of 5 in 31520332 is

maths numbers and place value face value of digit large numbers general form of number

  1. 49998

  2. 499995

  3. 49995

  4. none

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  The given number is $31520332$.

$\Rightarrow$   Face value of 5 in the given number is $5$.
$\Rightarrow$   Place value of 5 in the given number is $500000.$
$\therefore$   Place value - Face value  = $500000-5=499995$
$\therefore$    Required difference is $499995$.

The difference between the value and face value of $5$ in $91,25,678$ is

maths numbers and place value face value of digit large numbers general form of number

  1. $4995$

  2. $0$

  3. $4095$

  4. $5000$

Show answer
Correct Option: A
Explanation:

(A) Place value of 5 in 
$91,25,678=5000$
Face value of 5 in 
$91,25,678=5$
$\therefore :difference=5000-5$
$=4995$ 

Face value of 7 in 3728456

maths numbers and place value face value of digit large numbers general form of number

  1. 7,00,000

  2. 7000

  3. 7

  4. 70,000

Show answer
Correct Option: C
Explanation:

Face value of a digit in any place will be the digit itself.

Hence, the correct answer is 7.

Difference between the face values of 5 and 9 in 165,234 and 842,928 is

maths numbers and place value face value of digit large numbers general form of number

  1. 44

  2. 5900

  3. 4

  4. 14

Show answer
Correct Option: C
Explanation:

Face values of 5 and 9 are 5 and 9 respectively. 

Difference $= 9-5 = 4$