Question
In the given figure,
From the above figure, what is the value of x?
- 1
- 2
- 3
- All the above
Hint:
We know that in a triangle, the sum of two sides should be greater than the third. So, we will substitute the value of x and check if it satisfies the theorem.
The correct answer is: All the above
Given, AB=4x+5, BC=6x+5, CA= 5x+5
for x=1 for x=2 for x=3
AB=4+5=9 AB=8+5=13 AB=12+5=17
BC=6+5=11 BC=12+5=17 BC=18+5=23
CA=5+5=10 CA=10+5=15 CA=15+5=20
By substituting, we get all the values of x satisfy the property of the triangle inequality i.e. In a triangle, the sum of two sides should be greater than the third.
Related Questions to study
Which group of lengths is used to form a triangle?
Which group of lengths is used to form a triangle?
Mention the smaller angle to the larger angle from the given figure.
Mention the smaller angle to the larger angle from the given figure.
What is the possible length of AB in the given figure?
What is the possible length of AB in the given figure?
If one side of a triangle is 10 cm and another side is 6 cm. Find the possible length of the third side, if the third side is the longer side.
If one side of a triangle is 10 cm and another side is 6 cm. Find the possible length of the third side, if the third side is the longer side.
Mention the longer side to the smaller side from the given figure.
Mention the longer side to the smaller side from the given figure.
Can we draw a triangle for side lengths 5, 4, and 10 units? If so, mention the reason.
Can we draw a triangle for side lengths 5, 4, and 10 units? If so, mention the reason.
The angle opposite to the longer side is _____ in a triangle.
The angle opposite to the longer side is _____ in a triangle.
The sum of lengths of any two sides is ____ than the third side in a triangle.
The sum of lengths of any two sides is ____ than the third side in a triangle.
What can be the length of AB?
AB > 46
What can be the length of AB?
AB > 46
What can be the length of AC?
Therefore, the Side AC should be greater than 58 degrees.
What can be the length of AC?
Therefore, the Side AC should be greater than 58 degrees.
What do you observe in ∆ABC?
Right angled triangle:
The triangle in which one of the angle is being 90 degrees.
>>>Therefore, we can say that the given triangle is an example of right angled triangle.
What do you observe in ∆ABC?
Right angled triangle:
The triangle in which one of the angle is being 90 degrees.
>>>Therefore, we can say that the given triangle is an example of right angled triangle.
Which group of lengths is used to form a triangle?
The sides that follows triangle inequality is (3,4,5).
>>>It forms right angled triangle.
Which group of lengths is used to form a triangle?
The sides that follows triangle inequality is (3,4,5).
>>>It forms right angled triangle.
Mention the smaller angle to the larger angle from the given figure.
The required relation between the angles of a given triangle is:
∠CBA < ∠CAB < ∠ACB
Mention the smaller angle to the larger angle from the given figure.
The required relation between the angles of a given triangle is:
∠CBA < ∠CAB < ∠ACB
How can you say which angle is the largest in a triangle?
>>>By using the longest side largest angle theorem, we can find the largest angle in the triangle.
How can you say which angle is the largest in a triangle?
>>>By using the longest side largest angle theorem, we can find the largest angle in the triangle.
If one side of a triangle is 11 cm and another side is 6 cm. Find the possible length of the third side.
Let x be the length of the third side.
11 + 6 > x
17 > x
6 + x > 11
X > 5
The third side value can be greater than 5 and less than 17.
If one side of a triangle is 11 cm and another side is 6 cm. Find the possible length of the third side.
Let x be the length of the third side.
11 + 6 > x
17 > x
6 + x > 11
X > 5
The third side value can be greater than 5 and less than 17.
