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Question 124
The perimeter of a triangle is 40cm and its area is 60 cm$$^2$$ . If the largest side measures 17cm, then the length (in cm) of the smallest side of the triangle is
Solution
Given that , a+b+c = 40 . So , s = $$\frac{a+b+c}{2}$$ = 20 . Also , 17+b+c = 40 i.e. b+c = 23 i.e. c=23-b
Area = 60 = $$\sqrt{s(s-a)(s-b)(s-c)}$$ = $$\sqrt{20(20-17)(20-b)(20-(23-b))}$$
b= 8
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