Question

The sides of a triangle measure 3√6,2√24,and 7√54 what is the perimeter of the triangle

Answer 1

To find the perimeter of a triangle, you simply add the lengths of its sides together. The sides you provided are:

1. \( 3\sqrt{6} \)
2. \( 2\sqrt{24} \)
3. \( 7\sqrt{54} \)

Now, let's simplify each side:

1. **For \( 2\sqrt{24} \)**:
\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}
\]
Thus,
\[
2\sqrt{24} = 2 \cdot 2\sqrt{6} = 4\sqrt{6}
\]

2. **For \( 7\sqrt{54} \)**:
\[
\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6}
\]
Thus,
\[
7\sqrt{54} = 7 \cdot 3\sqrt{6} = 21\sqrt{6}
\]

Now, we have simplified the sides to:
- Side 1: \( 3\sqrt{6} \)
- Side 2: \( 4\sqrt{6} \)
- Side 3: \( 21\sqrt{6} \)

Now we can calculate the perimeter by adding these together:
\[
\text{Perimeter} = 3\sqrt{6} + 4\sqrt{6} + 21\sqrt{6}
\]
Combine like terms:
\[
\text{Perimeter} = (3 + 4 + 21)\sqrt{6} = 28\sqrt{6}
\]

Thus, the perimeter of the triangle is \(\boxed{28\sqrt{6}}\).