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The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?
Correct answer is '2'. Can you explain this answer?
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Solution: An isosceles triangle has two sides equal. We have three cases:
Case (i): x + 7 = 9 - 2x
3x = 2. x = 2/3, which is not an integer.
Case (ii): x + 7 = 3x - 1
2x = 8, x = 4
The sides are 11,11 and 1
Case (iii): 9 - 2x = 3x - 1, 5x = 10, x = 2 The sides are 5, 5 and 9
The triangle is isosceles for two values of x.
Answer: 2
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Solution: An isosceles triangle has two sides equal. We have three cases:Case (i): x + 7 = 9 - 2x3x = 2. x = 2/3, which is not an integer.Case (ii): x + 7 = 3x -12x = 8, x = 4The sides are 11,11 and 1Case (iii): 9 - 2x = 3x - 1, 5x = 10, x = 2 The sides are 5, 5 and 9The triangle is isosceles for two values of x.Answer: 2
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