Triangle Inequality 1

Q. Question 8
Two sides of a triangle are of length 5 cm and 1.5 cm. The length of the third side of the triangle cannot be
(A) 3.6 cm
(B) 4.1 cm
(C) 3.8 cm
(D) 3.4 cm

Q. If two sides of a triangle are 8cm and 13cm, then the length of the third side lies between $a$ cm and $b$ cm. Find the values of $a$ and $b$ such that $a$ is less than $b$ .

1. a=5 cm and b=13 cm
2. a=8 cm and b=21 cm
3. a=21 cm and b=5 cm
4. a=5 cm and b=21 cm

Q. Which of the following is correct regarding the figure given below?

1. AC < CD < BC
2. CD < AC < BC
3. BC < AC < CD
4. AC < BC < CD

Q. Find the correct order of length of sides in the following triangle.

1. AB < AC < BC
2. AB < BC < AC
3. BC < AB < AC
4. AB > AC > BC

Q.

The lengths of the sides of a triangle are 5 cm, 12 cm and 13 cm. The length of the perpendicular from the opposite vertex to the side whose length is 13 cm is $\frac{m}{13}$. Find the value of $m÷10$.

1. 6

2. 60

3. 5

4. 13

Q.

Is it possible to have a triangle with the following side lengths ?

17cm, 7cm, 8cm

Q.

The difference between the lengths of any two sides of a triangle is smaller than the length of the third side. State whether the statement is True or False.

1. True
2. False

Q. If the minimum distance from its opposite side of an equilateral triangle is $4\sqrt{3}$ cm, then determine the side length of the triangle.

1. 8 cm
2. 10 cm
3. 12 cm
4. 6 cm

Q.

Two sides of a triangle are of length $5cm$ and $1.5cm$. Which of the following cannot be the length of the third side of the triangle?

1. $4.3cm$
2. $6.5cm$
3. $3.6cm$
4. $4cm$

Q.

In $△ABC$, $\angle ABC={30}^{\circ }$ and $\angle ACB={45}^{\circ }$. Which is the longest side in this triangle?

1. All sides are same in length

2. AB

3. BC

4. CA

Q. In the figure below, if AC$>$AB and D is point on AC such that AB = AD, then which of the following relation is true between BC and CD?

1. BC = CD
2. BC > CD
3. BC < CD
4. BC $\le$ CD

Q. ABC is a triangle such that $AB=20cm$ and $AC=5cm$.
Then, which of the following is true about the side BC?

1. 15 < BC < 25
2. 10 < BC < 25
3. 10 < BC < 30
4. 15 < BC < 30

Q.

In a right angle triangle board the difference between the two sides containing right angle is 2m and the area of the triangle is 60 $m^2$.Find the base and height of the triangle. [3 MARKS]

Q. ABC is an isosceles triangle, where sides AB and AC are equal. If AB = AC = 8 cm and BC =12 cm, find the minimum distance of vertex A from the side BC.

1. $2\sqrt{7}$ cm
2. $3\sqrt{7}$ cm
3. $4\sqrt{7}$ cm
4. $5\sqrt{7}$ cm

Q. In the following figure, ED = EC. Then, which of the following are true?

1. $BE>BD+EC$
2. $AB+AD>BE+EC$
3. $BC>BD$
4. $BD>BE+EC$

Q. In the figure given below, prove that BC < AC < CD.

Q.

In any triangle ABC, (AB - AC) $>$ BC.

1. - =

2. AB – AC = BC

Q.

In the following figure, ED = EC. Then, which of the options is/are true?

1. 180°

2. 360°

3. 90°

4. 270°

Q. Is it possible to have a triangle with the following sides
(i) $2cm,3cm,5cm$
(ii) $3cm,6cm,7cm$
(iii) $6cm,3cm,2cm$

Q.

In the triangle below, which arrangement below has the sides in the ascending order of their length?

1. AB, CA, BC

2. AC, AB, BC

3. AB, BC, CA

4. CA, BC, AB

Q.

State which of the following sets of side lengths will form a triangle?

$4mm,19mm,12mm$

Q.

In the given figure, ∆ABC is a triangle. If ∠ACB=(3x-10)°, ∠CAB=50°, and ∠ABC=(x+20)° . What is the value of x?

1. 30°

2. 40°

3. 60°

4. 50°

Q.

Use the following figure to find: DF, if CG = 11 cm.

1. 2.5 cm
2. 5.5 cm
3. 6.5 cm
4. 9.5 cm

Q.
In the given figure, the shortest distance of point A from line $l$ is ____.

1. AB
2. AC
3. AD
4. AE

Q. If the two sides of a triangle are unequal, then the larger side has the smaller angle opposite to it.

Q. In $\Delta ABC$, if ∠A = 45° and ∠B = 65°, then the longest side of the triangle is .

1. AB
2. BC
3. CA

Q.

If two angles of a triangle are unequal, the greater angle has the smaller side opposite to it

1. True

2. False

Q. The lengths of two sides of a triangle are $12$ cm and $15$ cm. Between what two measures should the length of the third side fall?

1. $3and27$
2. $5and20$
3. $10and12$
4. $8and12$

Q. Calculate the value of $x$ in the given figure.

Q. In the adjoining figure, the point $D$ divides the side $BC$ of $△ABC$ in the ratio $m:n$. Prove that $ar\left(△ABD\right):ar\left(△ADC\right)=m:n$.