Question

The length of the sides of ΔABC are consecutive intergers. It ΔABC has the same perimeter as an equilateral triangle, triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?
A. 4
B. 6
C. 8
D. 10

Answer 1

The length of the shortest side of  ΔABC is :

C. 8

• Let us consider the perimeter of an equilateral triangle is "A" and each of its sides is "a".

• Therefore, A = a+a+a

                             = 3a

                             = 3(9)                                  (as per the question, a=9)

                             = 27 cm

• Now, let us consider that the 3 sides of triangle (ΔABC) is-

        s (AB) , s+1 (BC) , s-1 (CA)

• And, perimeter of triangle (P) = AB+BC+CA

                                                         = s + s+1 + s-1

• As per the question, A = P

• Therefore, 27 =  s + s+1 + s-1

                          27 = 3s

                            s = 9

• Therefore, the sides of triangle are :

         s = 9

         s+1 = 10

         s-1 = 8

• Thus the shortest side is 8 cm.