Question

Classify the triangle in Example 2 by its side lengths.

Short answer

It is a scalene triangle.

Step-by-step solution

Step 1. Given Information.

Perimeter of the triangle is given as 65 cm.

Length of third side is given as 20 cm.

Length of first side is twice the length of the second side.

Step 2. Calculation.

Let the length of the first side be x.

Length of the second side will be 2x.

Hence, this gives us,

$x+2x+20=65$

Add both x together.

$3x+20=65$

Subtract 20 from both the sides.

$3x+20-20=65-20$

This gives us,

$3x=45$

Now, divide both sides by 3.

$\frac{3x}{3}=\frac{45}{3}$

This will give us,

$x=15$

So, the length of first side is 15 cm.

Length of the second side is 2x, multiply 2 with 15.

$2\times 15=30$

So, the length of the second side is 30 cm.

Length of third side is given as 20 cm.

Step 3. Conclusion.

Since, all the three sides of the triangle are different it is a scalene triangle.