Question

The perimeter of triangle ABC is 54. the triangle has side lengths AB=3x, BC=4x, AC=5x. Find the length of each side.

Answer 1

The perimeter of a triangle is the sum of its sides. So, we have

`P = \overline{AB}+\overline{BC}+\overline{AC}`

We have an exact value for the perimeter, and variable expressions for the sides. Let's substitute the formula above with what we're given:

`54 = 3x+4x+5x = 12x`

If you divide both sides by 12, you have

`x = (54)/(12) = 4.5`

So, the lengths of the sides are

`AB = 3x = 3* 4.5 = 13.5`

`BC = 4x = 4* 4.5 = 18`

`AC = 5x = 5* 4.5 = 22.5`