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The sides of a triangle are consecutive integers. The perimeter of the triangle is 120 cm. Find the length of the greatest side :
Answer & Solution
Correct Answer:
Option
C
Let the sides of the triangles be x cm, (x + 1) cm and (x + 2) cm respectively.
Then,
$$\eqalign{ & x + \left( {x + 1} \right) + \left( {x + 2} \right) = 120 \cr & \Rightarrow 3x + 3 = 120 \cr & \Rightarrow 3x = 117 \cr & \Rightarrow x = 39 \cr} $$
∴ Length of greatest side :
= (39 + 2) cm
= 41 cm
Then,
$$\eqalign{ & x + \left( {x + 1} \right) + \left( {x + 2} \right) = 120 \cr & \Rightarrow 3x + 3 = 120 \cr & \Rightarrow 3x = 117 \cr & \Rightarrow x = 39 \cr} $$
∴ Length of greatest side :
= (39 + 2) cm
= 41 cm
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