Q. 214.4( 5 Votes )
The lengths of the sides of triangle ABC are consecutive integers. If triangle ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of triangle ABC?
Answer :
To Find: the shortest side of triangle ABC
Given: Length of the sides of a triangle are consecutive integers.
The perimeter of triangle = Perimeter of an equilateral triangle of side length 9 cm.
Concept Used:
If sides of a triangle are a, b, and c, then area of a triangle is given by:
Where s = semiperimeter of the triangle
Perimeter of equilateral triangle = 3 × side
Assumption:
Let the sides of the triangle be (x – 1), x, and (x + 1).
Explanation:
Perimeter of equilateral triangle = 3 × 9 cm = 27 cm
The perimeter of the given triangle = 27 cm
x – 1 + x + x + 1 = 27 cm
3 x = 27 cm
x = 9 cm
Therefore, the sides of the triangle are:
(x – 1) = (9 – 1) cm = 8 cm
x = 9 cm = 9 cm
(x + 1) cm = (9 + 1) cm = 10 cm
Now calculate the area of this triangle,
Hence, the area of the triangle is 
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