Tag: congruence and inequalities of triangles

Quizzes (1) Questions (47)

Questions Related to congruence and inequalities of triangles

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

Two sides of a $\Delta$ le are $7$ and $10$ units. Which of the following length can be the length of the third side?

  1. $19$ cm
  2. $17$ cm
  3. $13$ cm
  4. $3$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given that the two sides of triangle  are $7$ and $10$.

Sum of two sides $= 17$
Difference between two sides $= 3$
Therefore, the third side should be between $3$ and $17$ and only one option satisfies it i.e Option C.

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

If A is the area of a triangle in em", whose sides are 9 em, 10 cm and 11 em, then which one of the following is correct?

  1. $A < 40\:cm^2$
  2. $40\:cm^2 < A < 45\:cm^2$
  3. $45\:cm^2 < A < 50\:cm^2$
  4. $A>50\:cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle s=\frac{1}{2}(9+10+11):cm=15:cm$

$\therefore\Delta=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{15\times6\times5\times4}:cm^2$

$=30\sqrt{2}=30\times1.4=42:cm^2$
which lies between $40:cm^2$ and $45:cm^2$.

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

ABCD is a quadrilateral. Then which of the following is true? 

  1. $\displaystyle AC+BC<(AB+BC+CD+DA)$
  2. $\displaystyle AC+BD<\frac { 1 }{ 2 } \left( AB+BC+CD+DA \right) $
  3. $\displaystyle AC+BD>\frac { 1 }{ 4 } \left( AB+BC+CD+DA \right) $
  4. $\displaystyle AC+BD<\frac { 1 }{ 4 } \left( AB+BC+CD+DA \right) $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle AB+BC>AC$ (considering $\displaystyle \Delta ABC$)
$\displaystyle BC+CD>BD$ (considering $\displaystyle \Delta BCD$)
$\displaystyle CD+DA>AC$ (considering $\displaystyle \Delta ADC$)
$\displaystyle DA+AB>BD$ (considering $\displaystyle \Delta ABD$)
Adding all four inequalities, we get
$\displaystyle 2(AB+BC+CD+DA)>2(AC+BD)$
$\displaystyle AB+BC+CD+DA>AC+BD$

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

Two sides of a triangle have lengths $7$ and $9$. Which of the following could not be the length of the third side?

  1. $4$
  2. $5$
  3. $7$
  4. $11$
  5. $16$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

An important rule to remember about triangles is called the third side rule: the length of the third side of a triangle is less than the sum of the lengths of the other two sides and greater than the (positive) difference of the lengths of the other two sides. 

For this triangle, the length of the third side must be greater than $9-7=2$97=2 and less than $9+7=16$9+7=16. All the answers are possible except for answer E, which is equal to $16$16 but not less than $16$16.

Multiple choice maths congruence and inequalities of triangles inequalities of a triangle triangle inequality inequalities in triangle

Which of the following sets of measurements can be used to construct a triangle?

  1. $4\ cm, 5\ cm, 6\ cm$
  2. $4\ cm, 3\ cm, 8\ cm$
  3. $5\ cm, 6\ cm, 12\ cm$
  4. $6\ cm, 3\ cm, 10\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Because the sum of the length of any $2$ sides of the triangle should be greater than the third side, which is only satisfied by option 1.

$(4+5)>6$
$(4+6)>5$
$(5+6)>4$