Triangle Inequality

Q.

ABCD is quadrilateral. Is AB+BC+CD+DA<2(AC+BD)?

Q. The three side lengths of a non-degenerate triangle are $x$, $x+5$ and $x+11$. Then $x$ cannot be .

1. $4$
2. $8$
3. $7$
4. $10$

Q. The lengths of two sides of a triangle are $6cm$ and $8cm$. Between which two numbers can the length of the third side fall? (assuming the length of the third side to be $xcm$ )

1. $2\le x\le 14$
2. $2<x<14$
3. $4\le x\le 12$
4. $3<x<14$

Q. In a triangle $△ABC$, which of the following statement is correct?

1. $AB+BC<AC$
2. $AB+BC=AC$
3. $AB+BC>AC$
4. All are correct

Q.

ABCD is quadrilateral.

Is AB + BC + CD + DA < 2 (AC + BD)?

Q. The triangle has sides as $12$ cm, $6$ cm and $4$ cm. The triangle is a/an -

1. Isosceles Triangle
2. Scalene Triangle
3. Equilateral Triangle
4. Triangle cannot be formed

Q. For any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

1. Yes
2. No

Q. Can the altitudes and medians be same for a triangle?

Q. The lengths of two sides of a triangle are $6cm$ and $8cm$. Between which two numbers can the length of the third side fall? (assuming the length of the third side to be $xcm$ )

1. $2\le x\le 14$
2. $2<x<14$
3. $4\le x\le 12$
4. $3<x<14$

Q.
$p,q,r$ are the sides of the triangle $PQR$ as shown. If $q=5$ units and $r=10$ units, then $p=$

1. $5$ units
2. $4$ units
3. $10$ units

Q. Measurements of sides of some triangles are given.
Which of the following triangle(s) can be formed with the given measurements ?

1. $△ABC$ in which $AB=4\text{cm},BC=5\text{cm}\&AC=0.5\text{cm}$
2. $△ABC$ in which $AB=10\text{cm},BC=5\text{cm}\&AC=7\text{cm}$
3. $△ABC$ in which $AB=4\text{cm},BC=4\text{cm}\&AC=5\text{cm}$
4. $△ABC$ in which $AB=10\text{cm},BC=4\text{cm}\&AC=4\text{cm}$

Q. The side lengths of a non-degenerate triangle $ABC$ are $4$, $11$ and $c$. The value of $c$ is

1. $15$
2. $7$
3. $17$
4. $12$

Q. Rashil walked around the triangular park and remembered that two of the park's sides were $60\text{m}\&65\text{m}$. He forgot to measure the third side. Finally, he tried to estimate the length of third side. Choose the correct estimation. Let third side be $a$

1. $5\text{m}<a<125\text{m}$
2. $125\text{m}<a$
3. $5\text{m}\le a\le 125\text{m}$
4. All the above are possible.

Q. $ABC$ is a traingle having two of its sides as $15.6$ cm and $10.6$ cm. Also, $15.6$ cm side length is the largest one. The third side of triangle will be -

1. equal to $5$ cm.
2. less than $5$ cm.
3. greater than $5$ cm.
4. any dimension.

Q. For any number $x$, is it possible to construct a triangle with the side lengths as $x,2x\&4x$?

1. Yes
2. No

Q. If $x$ is some natural number, can a triangle have sides measuring $x,2x\&3x$?

1. Yes
2. No

Q. AM is a median of a triangle ABC. Is AB + BC + CA $>$ 2AM?

Q. $p,b,c$ are the side lengths of a triangle $ABC$ with $b=4$ units and $c=8$ units, then

1. $4<p<12$
2. $3<p<15$
3. $4<p<15$

Q. ABCD is quadrilateral.
Prove that (AB + BC + CD + DA) > (AC + BD)

Figure

Q.

Choose the correct answer.

The middle-sized angle is always opposite to the ______ side.

1. Largest

2. Smallest

3. Middle

Q. For the given side lengths, for which of the following a triangle can be formed:
A. $9,3,5$
B. $1,2,3$
C. $10,8,6$

1. A. $9,3,5$
2. B. $1,2,3$
3. $10,8,6$
4. None of these.

Q. Construct an isosceles triangle $PQR$ in which base $PQ=7.2cm$ and altitude from R on $PQ$ is $5cm$

Q. In triangle ABC, BC = 6 cm and ED || BC, joins the midpoints of other two sides. Find ED.

1. 3 cm
2. 12 cm
3. 6 cm
4. 4 cm

Q. A triangle can have sides of any arbitrary length.

1. True
2. False