Question

The lengths of the sides of $\Delta ABC$ are consecutive integers. If $\Delta ABC$ has the same perimeter as an equilateral triangle with a side of length $9cm$, what is the length of the shortest side of $\Delta ABC$ ?

• A. $10$
• B. $4$
• C. $8$
• D. $6$

Answer 1

The correct option is C $8$

Given: Side of an equilateral triangle $=9cm$

$\therefore \text{Perimeter of an equilateral triangle}=9\times 3$
$=27cm$

Since the sides of $\Delta ABC$ are consecutive integers,
Let the sides of $\Delta ABC$ be $AB=x,BC=x+1,AC=x+2$

Since, perimeter of $\Delta ABC=$ Perimeter of equilateral triangle
$\Rightarrow x+(x+1)+(x+2)=27$
$\Rightarrow 3x=27-3$
$\Rightarrow x=24$
$\Rightarrow x=8cm$

Hence, $\left(c\right)$ is the correct answer.