Question

The second side of the triangle is 2 cm larger than the first, and the third side is twice as large as the first side. If the perimeter of this triangle is 26 cm, find the length of its larger side.

Answer 1

To solve for the largest side of the triangle, we set up an equation using the given perimeter and the relationships between the sides. After solving for the smallest side, we find that the length of the largest side is 12 cm.

Step-by-step explanation:

The question asks to find the length of the largest side of a triangle given its perimeter and the relationships between the side lengths.

Let's define the sides of the triangle as follows: the first side as x cm, the second side as x + 2 cm (2 cm larger than the first), and the third side as 2x cm (twice as large as the first).

The perimeter of the triangle is the sum of its sides, which is given as 26 cm.

Now, we can write an equation to represent the perimeter:

• x + (x + 2) + 2x = 26 cm

Simplifying this equation:

• 4x + 2 = 26
• 4x = 24
• x = 6

Now that we know the first side is 6 cm, we can find the length of the largest side:

The largest side is 2x, which is 2 × 6 cm = 12 cm.

Therefore, the length of the largest side of the triangle is 12 cm.