Tag: construction of triangles - ii

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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 maths geometrical constructions construction of triangles constructions of triangles construction of triangles - ii

To construct a triangle similar to a given triangle ABC with its sides 6/5th of the corresponding sides of $\Delta$ABC. Correct order of steps of construction -
(a) Draw a ray AX inclined at certain angle with AB on opposite side of C.
(b) Starting from A, cut off six equal line segments AX$ _1$, X$ _1$X$ _2$, X$ _2$X$ _3$, X$ _3$X$ _4$, X$ _4$X$ _5$ and X$ _5$X$ _6$ on AX.
(c) Draw a line B'C' parallel to BC to intersect AC produced at C'
(d) Join X$ _5$B and draw a line X6B' parallel to X5B, to intersect AB produced at B'.

  1. abcd

  2. acbd

  3. abdc

  4. adcb
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To construct a triangle like the one given in the following question, the given steps are to be followed:

1. Draw a ray AX inclined at a certain angle with AB on opposite side of C.
2. Starting from A, cut off six equal line segments $AX _1, X _1X _2, X _2X _3, X _3X _4, X _4X _5 and X _5X _6$ on $AX$.
3. Join $X _5B$ and draw a line $X _6B'$ parallel to $X _5B$, to intersect $AB$ produced at $B'$.
4.Draw a line $B'C'$ parallel to $BC$ to intersect $AC$ produced at $C'$.

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

Construct a $\Delta ABC$, whose perimeter is $10.5  cm$ and base angles are $60^o$ and $45^o$. Find the third angle.

  1. $75^o$
  2. $45^o$
  3. $90^o$
  4. $60^o$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
  1. Draw a line segment PQ such that AB + BC + AC = PQ.
    2. Construct $\angle XPQ =\angle B = { 60 }^{ 0 }\ and\ \angle YQP =\angle C =45^{ 0 }$
    3. Bisect $\angle XPQ and \angle YQP$ and their bisectors will meet at A.
    4. Draw the perpendicular bisector DE of AP which meets PQ  at B. 
    5. Draw the perpendicular bisector FG of AQ which meets PQ  at C.
    6. Join AB & AC.
    7. ABC is the required triangle.
    Sum of interior angle of triangle= $180^o$
    so third angle = $180^o-45^o-60^o\ = 75^o $