Triangle with sides in terms of x
Triangle with sides in terms of x
IP 2
8 marks
A triangle has sides of length \((x+3)\) cm, \((2x-1)\) cm and \((11-x)\) cm. In any triangle, the sum of the lengths of any two sides is greater than the length of the third side.
- Find the range of values of \(x\) for which such a triangle exists.[4]
- Given that \(x\) is an integer and the perimeter of the triangle is at most \(25\) cm, list the possible values of \(x\).[2]
- Show that if the triangle is isosceles, then it must be equilateral.[2]
Solution:
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Answer:(a) \(\dfrac{9}{4}<x<\dfrac{15}{2}\) (b) \(3,4,5,6\) (c) Each equal pair gives \(x=4\): sides \(7\), \(7\), \(7\)
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