Question

The perimeter of a triangle is $42$ yards. The first side is $5$ yards less than the second side, and the third side is $2$ yards less than the first side.

What is the length of each side?

Answer 1

Finding the length of each side:

Step-1: Assumption

Let the length of the second side of the triangle be $x$ yards.

Since, the first side is $5$ yards less than the second side, the length of the first side will be $x-5$ yards.

Again, since, the third side is $2$ yards less than the first side, the length of the third side will be $x-5-2=x-7$ yards.

Step-2: Finding value of $x$

As the length of the three sides of the triangle are $x$ yards, $x-5$ yards and $x-7$ yards, so, the perimeter will be

$$\begin{gathered} S=x+x-5+x-7 \\ =3x-12\text{yards} \end{gathered}$$

But given that the perimeter of the triangle is $42$. So, we must have :

$$\begin{gathered} 3x-12=42 \\ \Rightarrow 3x=42+12 \\ \Rightarrow x=\frac{54}{3} \\ \therefore x=18 \end{gathered}$$

Step-3: Finding the lengths of the three sides

Since, $x=18$, the length of the first side will be

$$\begin{gathered} l_1=x-5 \\ =18-5 \\ =13\text{yards} \end{gathered}$$

The length of the second side will be $l_2=x=18\text{yards}$.

The length of the third side will be

$$\begin{gathered} l_3=x-7 \\ =18-7 \\ =11\text{yards} \end{gathered}$$

Therefore, the lengths of the three sides of the given triangle are : $13$ yards, $18$ yards and $11$ yards respectively.