Question

A wire 100 cm long is bent to form a triangle. The middle-sized side of the triangle is 2 cm longer than one side and 6 cm shorter than the other side. What are the lengths of the three sides?

a) 20 cm, 22 cm, 58 cm
b) 30 cm, 32 cm, 38 cm
c) 24 cm, 26 cm, 50 cm
d) 28 cm, 30 cm, 42 cm

Answer 1

The lengths of the three sides of the triangle are approximately 34.67 cm, 36.67 cm, and 28.67 cm.

Step-by-step explanation:

Let's define the lengths of the three sides of the triangle as follows:

• Side A: x cm
• Side B: (x + 2) cm (2 cm longer than side A)
• Side C: (x - 6) cm (6 cm shorter than side B)

Since the wire used to form the triangle is 100 cm long, we can write an equation to represent the perimeter of the triangle:
Side A + Side B + Side C = 100 cm

Substituting the values we defined earlier, we get:
x + (x + 2) + (x - 6) = 100 cm

Simplifying the equation:
3x - 4 = 100 cm
3x = 104 cm
x = 34.67 cm

Therefore, the lengths of the three sides of the triangle are approximately:
Side A: 34.67 cm
Side B: 36.67 cm
Side C: 28.67 cm