Question

A triangle has a perimeter of 58 feet. If the three sides of the triangle are n, 3n+4, and 4n-10, what is the length of each side?

Answer 1

Alright, so we know that the sum of all sides of a triangle equals the triangle's perimeter. In this case, the perimeter is given as 58 feet.

The given sides of the triangle are n, 3n+4, and 4n-10.

So we can set up the equation as follows to find the value of 'n':

n + (3n+4) + (4n-10) = 58

This simplifies into:

8n - 6 = 58

We add 6 to each side of the equation to isolate the term with 'n' on one side:

8n = 64

We then divide each side by 8 to solve for 'n':

n = 8

So, we have the value of 'n'.

Remember, each side of the triangle is represented in terms of 'n'. We can substitute 'n' with 8 and find the length of each side:

1. The first side is simply 'n', which equals 8.

2. The second side is '3n+4', substituting 'n' with 8 we get:
3 * 8 + 4 = 28

3. The third side is '4n-10', again substituting 'n' with 8 we get:
4 * 8 - 10 = 22

So, the lengths of the three sides of the triangle are 8 feet, 28 feet, and 22 feet respectively.

Answer 2

side lengths are 8, 28, and 22 feet

Explanation:

The perimeter is the sum of the lengths of the three sides:

58 = n + (3n+4) + (4n-10)

64 = 8n . . . . . collect terms, add 6

8 = n . . . . . . . .divide by 8. First side length

3n+4 = 3·8 +4 = 28 . . . . second side length

4n-10 = 4·8 -10 = 22 . . . . third side length

The side lengths are 8 ft, 28 ft, 22 ft.