A triangle has a perimeter of 51 feet. If the three sides of the triangle are n, 3n+4, and 3n−2, what is the length of each side?

Answer 1

The perimeter is the sum of the lengths of the 3 sides. And we know this is 51 feet.

Therefore, we can write the equation: n + (3n +4) + (3n - 2) = 51

Simplifying on the left: 7n + 2 = 51

7n = 49 [subtracting 2 from both sides]

So, n = 7 [dividing through by 7]

Therefore, the 3 sides are 7, 25, and 19, respectively [plugging n = 7 for each side]

Check: the sum of the 3 sides = 7 + 25 +19 = 51 as expected.

Answer 2

To find the perimeter of any shape, you add the length of each side.

Total perimeter = 51 ft = (n) + (3n+4) + (3n - 2)

Combine Like Terms

51 = 1n +3n + 3n + 4 - 2

51 = 7n + 2

Solve for n -> subtract 2 on both sides

51 -2 = 7n + 2 - 2

49 = 7n

Solve for n -> divide by 7 on both sides

49 ÷ 7 = 7n ÷ 7

7 = n

Plug in 7 for n for each side

side 1 = n = 7

side 2 = 3n + 4 = 3 x 7 + 4 = 21 + 4 = 25

side 3 = 3n - 2 = 3 x 7 - 2 = 21 - 2 = 19

Side 1 = 7 ft

Side 2 = 25 ft

Side 3 = 19 ft