A triangle has sides in the proportion of 3:4:5. If the perimeter is 48 cm, what is the length of the longest side?

In a triangle with sides in the proportion of 3:4:5, these numbers represent the lengths of the sides relative to each other. To find the actual lengths of the sides, we can denote the sides as 3x, 4x, and 5x, where x is a common factor.

To find the total perimeter of the triangle, we add the lengths of all three sides:

[

3x + 4x + 5x = 12x

]

Given that the perimeter is 48 cm, we set up the equation:

[

12x = 48

]

Solving for x gives:

[

x = \frac{48}{12} = 4

]

Now we can find the lengths of the sides:

• The side corresponding to 3 is ( 3x = 3 \times 4 = 12 ) cm.

• The side corresponding to 4 is ( 4x = 4 \times 4 = 16 ) cm.

• The side corresponding to 5 is ( 5x = 5 \times 4 = 20 ) cm.

The longest side of the triangle is thus 20 cm.