Question : The three sides of a triangle are 5 cm, 9 cm, and x cm. The minimum integral value of x is:
Option 1: 2
Option 2: 3
Option 3: 4
Option 4: 5
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Correct Answer: 5
Solution : Given: The three sides of a triangle are 5 cm, 9 cm, and $x$ cm. We know, the sum of two sides of a triangle is greater than the third side. So, $x$ < 5 + 9 ⇒ $x$ < 14 Again, we know the difference between the two sides of a triangle is less than the third side. So, $x$ > 9 – 5 ⇒ $x$ > 4 $\therefore$ 4 < $x$ < 14 So, the minimum value of x is 5. Hence, the correct answer is 5.
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Question : Possible lengths of the three sides of a triangle are:
Option 1: 2 cm, 3 cm, and 6 cm
Option 2: 3 cm, 4 cm, and 5 cm
Option 3: 2.5 cm, 3.5 cm, and 6 cm
Option 4: 4 cm, 4 cm, and 9 cm
Question : In $\triangle ABC$, $D$ and $E$ are points on sides $AB$ and $AC$, such that $DE$ II $BC$. If $AD=x+3$, $DB =2 x-3$, $A E=x+1$ and $EC=2 x-2$, then the value of $x$ is:
Option 1: $\frac{4}{5}$
Option 2: $\frac{1}{2}$
Option 3: $\frac{3}{5}$
Option 4: $\frac{1}{5}$
Question : In a right-angled triangle, if the hypotenuse is 20 cm and the ratio of the other two sides is 4 : 3, the lengths of the sides are:
Option 1: 4 cm and 3 cm
Option 2: 8 cm and 6 cm
Option 3: 12 cm and 9 cm
Option 4: 16 cm and 12 cm
Question : The lengths of the three sides of a triangle are 30 cm, 42 cm, and $x$ cm. Which of the following is correct?
Option 1: $12 \leq x<72$
Option 2: $12>x>72$
Option 3: $12<x<72$
Option 4: $12 \leq x \leq 72$
Question : Which of the set of three sides can't form a triangle?
Option 1: 5 cm, 6 cm, and 7 cm
Option 2: 5 cm, 8 cm, and 15 cm
Option 3: 8 cm, 15 cm, and 18 cm
Option 4: 6 cm, 7 cm, and 11 cm
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