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VARVARA [1.3K]
3 years ago
12

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

Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
7 0

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

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