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The length of the sides of a triangle are x + 1, 9 -x and 5x -3 . The number of values of x for which the triangle is isosceles is:
- a)0
- b)1
- c)2
- d)3
- e)4
Correct answer is option 'B'. Can you explain this answer?
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The length of the sides of a triangle are x + 1, 9 -x and 5x -3 . The...
In isosceles triangle, 2 sides will be equal
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Let x + 1 = 9 - x
2x = 8
X = 4
The sum of any two sides of triangle should be greater than third side
Hence, if x = 4, then sides of the triangle are 5, 5 and 17
This is invalid as the sum of (5+5) is less than 17
Let x + 1 = 5x - 3
X = 1
If x = 1, then the sides of the triangle are 2, 8, 2
This is also invalid
Let 9 - x = 5x - 3
X = 2
If x =2, then the sides of the triangle are 3, 7, 7
Hence, this is valid.
Most Upvoted Answer
The length of the sides of a triangle are x + 1, 9 -x and 5x -3 . The...
Explanation:
An isosceles triangle has two sides of equal length. Therefore, we need to find the values of x for which any two sides of the given triangle are equal.
Let's equate any two sides of the triangle and solve for x:
1. x + 1 = 9 - x (if x + 1 = 5x - 3, we get a negative value of x which is not possible)
=> 2x = 8
=> x = 4
2. x + 1 = 5x - 3
=> 4x = 4
=> x = 1
3. 9 - x = 5x - 3
=> 6x = 12
=> x = 2
Solution:
From the above calculations, we can see that there is only one value of x (i.e. x=4) for which the given triangle is isosceles. Therefore, the correct answer is option 'B'.
An isosceles triangle has two sides of equal length. Therefore, we need to find the values of x for which any two sides of the given triangle are equal.
Let's equate any two sides of the triangle and solve for x:
1. x + 1 = 9 - x (if x + 1 = 5x - 3, we get a negative value of x which is not possible)
=> 2x = 8
=> x = 4
2. x + 1 = 5x - 3
=> 4x = 4
=> x = 1
3. 9 - x = 5x - 3
=> 6x = 12
=> x = 2
Solution:
From the above calculations, we can see that there is only one value of x (i.e. x=4) for which the given triangle is isosceles. Therefore, the correct answer is option 'B'.
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The length of the sides of a triangle are x + 1, 9 -x and 5x -3 . The number of values of x for which the triangle is isosceles is:a) 0b) 1c) 2d) 3e) 4Correct answer is option 'B'. Can you explain this answer?
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