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

$x = \dfrac{54}{12} = 4.5$

So, the lengths of the sides are

$AB = 3x = 3\times 4.5 = 13.5$

$BC = 4x = 4\times 4.5 = 18$

$AC = 5x = 5\times 4.5 = 22.5$