Tag: constructions

Quizzes (6) Questions (134)

Questions Related to constructions

Multiple choice maths construction of triangles constructions of triangles construction of triangles - ii constructions

Construct a $\triangle ABC$ in which:
$AB= 5.4\ cm$, $\angle CAB= 45^{0}$ and $AC\, +\, BC= 9\ cm$. Then the length of $AC$ (in $cm.$) is:

  1. $4$
  2. $7$
  3. $5$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the construction method for a triangle with given base, base angle, and sum of other two sides, the length of AC is derived from the geometric properties of the resulting triangle. For these values, AC is 5 cm.

Multiple choice maths construction of triangles constructions of triangles construction of triangles - ii constructions

The construction of $\Delta LMN$ when $MN=7$ $cm$ and $m\angle M=45^\circ$ is not possible when difference of $LM$ and $LN$ is equal to:

  1. $4.5$
  2. $5.5$
  3. $6.5$
  4. $7.5$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The triangle inequality rule states that the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.


In $\triangle LMN$, if $MN=7 \ cm$ then $LM-LN<7 \ cm$

This is not possible, from the given options, if $LM-LN=7.5 \ cm$

Option D.

Multiple choice maths construction of triangles constructions of triangles construction of triangles - ii constructions

Which of the following could be the value of $AC-BC$ in the construction of a triangle $ABC$ in which base $AB = 5 cm, \angle A = 30^{\circ}$?

  1. $5.5$
  2. $5$
  3. $2.5$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The triangle inequality rule states that the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.


In $\triangle ABC$, if $AB=5 \ cm$ then $AC-BC<5 \ cm$

This is not, from the given options, if $AC-BC=2.5 \ cm$

Option C

Multiple choice maths construction of triangles constructions of triangles construction of triangles - ii constructions

The construction of $\Delta LMN$ when $MN=6$ $cm$ and $m\angle M=45^\circ$ is not possible when difference between $LM$ and $LN$ is equal to:

  1. $6.9$ $cm$
  2. $5.2$ $cm$
  3. $5$ $cm$
  4. $4$ $cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a triangle sum of length of $2$ sides is $>$ third side.

or 

Difference of length of two sides is less than third side.

$LM,MN,NL$ are the length of sides.

$|LM-NL|<MN$

$|LM-NL|<6$

So construction of triangle is not possible as $|LM-NL|=6.9cm$

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

ABC is a triangle, the point P is on side BC such that $3\bar{BP}=2\bar{PC}$, the point Q is on the line $\bar{CA}$ such that $4\bar{CQ}=\bar{QA}$. If R is the common point $\bar{AP}$ & $\bar{BQ}$, then the ratio in which the fine joining CR divides $\bar{AB}$ is?

  1. $2:5$
  2. $3:8$
  3. $4:1$
  4. $6:1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using Menelaus' Theorem or vector geometry, the intersection of cevians in a triangle can be solved by setting up ratios of segments on the sides.

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

If a straight line $y-x=2$ divides the region ${x}^{2}+{y}^{2}\le 4$ into two parts, then the ratio of the area of the smaller part to the area of the greater part is 

  1. $\pi-2 : 3\pi+2$
  2. $3\pi-4 : \pi+4$
  3. $\pi-3 : 3\pi+3$
  4. $3\pi-8 : \pi+8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The line divides the circle into two segments. The area of the circle is 4*pi. The line distance from the center is sqrt(2), which allows calculating the sector and triangle areas to find the ratio.

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

The line joining points $(3,5)$ and $(2,7)$ is divided by $X-$ axis in the ratio.

  1. $5:7$
  2. $3:2$
  3. $-5:7$
  4. $-3:2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A point on the X-axis has a y-coordinate of 0. Using the section formula, the y-coordinate is (m*y2 + n*y1) / (m+n) = 0. Solving 7m + 5n = 0 gives m/n = -5/7, indicating external division.

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

The point $(\dfrac{7}{4},\dfrac{7}{8})$ divides the line segment joining the points (4,-1) and (-2,4) internally in the ratio 3 : 5.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the section formula with points (4, -1) and (-2, 4) and ratio 3:5, the x-coordinate is (3*-2 + 5*4) / 8 = 14/8 = 7/4. The y-coordinate is (3*4 + 5*-1) / 8 = 7/8. The point matches.

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

A square sheet of paper $ABCD$ is so folded that $B$ falls on the mid point $M$ of $CD$. The crease will divide $BC$ in the ratio :

  1. $7:4$
  2. $5:3$
  3. $8:5$
  4. $4:1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a geometry problem involving folding a square. Let the side be 2. B is (2,2), M is (1,0). The crease is the perpendicular bisector of BM. Solving for the intersection with BC gives the ratio.