Tag: maths

Questions Related to maths

Mark the correct alternative of the following.
In which of the following cases, a right triangle cannot be constructed?

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $12$cm, $5$cm, $13$cm

  2. $8$cm, $6$cm, $10$cm

  3. $5$cm, $9$cm, $11$cm

  4. None of these

Show answer
Correct Option: C
Explanation:

Any triangle is right angled if it satisfies $a^2 + b^2 = c^2$, where c is the largest side from option (A)  we take 

$a = 12 cm$
$b = 5 cm$
$c = 13 cm$
we know $(12)^2 + (5)^2 = 169 = (13)^2$
So we can construct a right angled triangle.

Similarly in option (B) we can take 
$a = 8 cm$
$b = 6 cm$
$c = 10 cm$
with these sides also we can construct a right angled triangle.

Consider option (C) then 
$a = 5 cm$
$b = 9 cm$
$c = 11 cm$
$a^2 + b^2 = 25 + 81$   But  $c^2 = 121$
             $= 106$

So we cannot construct right angled triangle from $5 cm, 9 cm, 11 cm$.

Construct a $\triangle PQR$ in which $QR= 4.6\ cm., {\angle Q}={\angle R=50 ^{0}}$. Then the perimeter of the triangle is:

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $10.2\ cm$

  2. $13.2\ cm$

  3. $11.8\ cm$

  4. $12.4\ cm$

Show answer
Correct Option: C

Construct a right angled $\triangle ABC$ with $\angle B = 90^\circ, BC = 5\ cm$ and $AC = 10\ cm$ and find the the length of side $AB$

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $6.2\ cm$

  2. $5\ cm$

  3. $8.7\ cm$

  4. $7.2\ cm$

Show answer
Correct Option: C
Explanation:

Step 1. Draw a line segment $BC=5\ \ cm$

Step 2. At $B$ draw an angle of $90^{\circ}$ and extend the ray.
Step 3. Now taking $C$ and centre draw an arc of radius $10$ cm intersecting the previous ray at $A$.
Step 4. Join $C$ to $A$.
Now using a ruler measure $AB$
$AB=8.7$ cm

Construct a $\triangle PQR$ such that $\angle P = 30^\circ, \angle Q = 60^\circ$ and $PQ = 10\ cm$.Find the measure of $\angle R$
maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $30^\circ$

  2. $45^\circ$

  3. $60^\circ$

  4. $90^\circ$

Show answer
Correct Option: D

Length of two sides of a $\triangle ABC$ is $AB=6\ cm$ and $BC=7\ cm$. Then, which of the following can represent the third side of the triangle ? Also, construct the triangle formed by these three sides.

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $8\ cm$

  2. $13\ cm$

  3. $14\ cm$

  4. $15\ cm$

Show answer
Correct Option: A
Explanation:

A triangle can be formed if sum of any two sides is greater then the third side.

Here $AB=6$ cm and $BC=7$ cm
Now $AB+BC>AC$
$6+7>AC$
$AC<13$ cm
So only option $A$ is possibel.
Steps of construction

Step 1. Draw a line segment $AB=6\ \ cm$
Step 2. Assuming $A$ a centre draw an arc of radius $8 \ \ cm$
Step 3. Now assuming $B$ as centre draw an arc of $7 \ \ cm$ intersecting the previous arc at $C$.
Step 4. Now join $A$ to $C$ and $B$ to $C$.

The perimeter of a triangle is $45\ cm$. Length of the second side is twice the length of first side. The third side is $5$ more than the first side. Find the length of each sides and construct the triangle made by these three sides.

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $11,19,15$

  2. $10,20,15$

  3. $10,16,19$

  4. $13,15,17$

Show answer
Correct Option: B
Explanation:

Let the length of first side $=x$

Length of second side $=2x$
Length of third side $=x+5$
Perimeter $=45cm$
$x+2x+x+5=45\ 4x=45-5\ 4x=40\ x=10$
So the sides are
$x=10$
$2x=2\times 10=20\ x+5=10+5=15$
Option $B$ is correct.

Construct a triangle $ABC$ in which $AB = 5 cm$ and $BC = 4.6 cm$ and $AC = 3.7 cm$
Steps for the construction is given in jumbled form.Choose the appropriate sequence for the above
1) With radius as $5\ cm$ from $C$, cut an arc.
2)They arcs will intersect at point $A$. Join $AB$ and $AC$. $ABC$ is the required triangle.
3)Draw a line segment $BC = 4\ cm.$
4)With radius as $3$ cm from $B$, cut the arc. 

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $1,4,3,2$

  2. $4,3,2,1$

  3. $3,1,4,2$

  4. $4,1,3,2$

Show answer
Correct Option: C
Explanation:

Correct sequence is:

1. Draw a line segment $AB=4$ cm.
2. With radius $5$ cm from $C$ , cut an arc.
3. With radius $3$ cm from $B$ , cut an arc.
4. The arc will intersect at point $A$, Join $AB$ and $AC$ .$ABC$ is required triangle.
So correct sequence is $3,1,4,2$
So option $C$ is correct.

Construct an isosceles $\triangle  XYZ,$ where $YZ=5$ units and $\angle XYZ=35^{o}$. Also, find the measure of $\angle YXZ$.

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $35^{o}$

  2. $70^{o}$

  3. $110^{o}$

  4. $140^{o}$

Show answer
Correct Option: C
Explanation:

$YZ=5$ CM $,\angle XYZ=35^{\circ}$

As the triangle is isosceles therefore $\angle XZY=50^{\circ}$
Steps of construction:
1. Draw a line segment $XY=5$ cm.
2. At $Y$ draw an angle of $35^{\circ}$ and extend the arm.
3. At $Z$ draw an angle of $35^{\circ}$ and extend the ray such that it intersect the previous ray at $X$
4. Join $Y$ to $X$ and $Z$ to $X$
Now measure $\angle YXZ$
$\angle YXZ=110^{\circ}$

Construct an isosceles $\triangle  ABC,$ where base $AB=7\ cm$ and $\angle ABC=50^{o}$. Also, find the measure of $\angle ACB$.

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $50^{0}$

  2. $80^{o}$

  3. $100^{o}$

  4. $120^{o}$

Show answer
Correct Option: B
Explanation:

$AB=7$ cm $,\angle ABC=50^{\circ}$

As the triangle is isosceles therefore $\angle CAB=50^{\circ}$
Steps of construction:
1. Draw a line segment $AB=7$ cm.
2. At $A$ draw an angle of $50^{\circ}$ and extend the arm.
3. At $B$ draw an angle of $50^{\circ}$ and extend the ray such that it intersect the previous ray at $C$
4. Join $A$ to $C$ and $B$ to $C$
Now measure $\angle ACB$
$\angle ACB=80^{\circ}$

For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the fourth step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass .
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle. 
5. Draw the base side $ QR = 6\  cm $.

maths construction of triangle construction of triangles - i construction of triangles constructions of triangles

  1. $5$

  2. $1$

  3. $2$

  4. $3$

  5. $4$

Show answer
Correct Option: D
Explanation:

Step 1. Draw a line $QR=6\ \ cm$

Step 2. At point $Q$ ,draw an angle of $90^{\circ}$
Step 3. From $R$ cut an arc $PR=10\ \ cm$ using compass.
Step 4. Name the point of intersection of the arm of angle $90^{\circ}$ and the arc in step $3$ , as $P$
Step 5. Join $P$ to $Q$. $PQR$ is required triangle.
So the fourth step is $3$
Option $D$ is correct.