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In English / Middle School | 2014-10-13

The perimeter of triangle ABC is 54. The triangle has side lengths \( AB = 3x \), \( BC = 4x \), and \( AC = 5x \).

Find the length of each side.

Asked by xax

Answer (3)

The perimeter is all the sides added together so: 3x + 4x + 5x = 54. 12x = 54. x = 54/12. x = 4.5. Then AB = 3 x 4.5. BC = 4 x 4.5. AC = 5 x 4.5. AB = 13.5, BC = 18, AC = 22.5.

Answered by W0lf93 | 2024-06-11

The problem involves finding the lengths of the sides of a triangle with a given perimeter and proportional side lengths. The sides of the triangle ABC are given as AB = 3x, BC = 4x, and AC = 5x. The total perimeter of the triangle is 54. To find the lengths of each side, we first add the sides to get the total perimeter in terms of x: 3x + 4x + 5x = 12x. Since the total perimeter is 54, we set this equal to 54 to solve for x: 12x = 54.
Dividing both sides of the equation by 12, we find that x = 4.5. With the value of x, we can then find the lengths of each side: AB = 3x = 13.5, BC = 4x = 18, and AC = 5x = 22.5.

Answered by JoaquinRafael | 2024-06-24

The lengths of the sides of triangle ABC are AB = 13.5, BC = 18, and AC = 22.5. We found these by setting up an equation for the perimeter, solving for x, and then multiplying x by the coefficients of each side length. Thus, we determined that x equals 4.5.
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Answered by W0lf93 | 2024-09-05

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