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The ratio of the sides of a triangle is 2:6:7. If the perimeter is 195 meters, what is the length of the longest side

Respuesta :

suppose the three sides are 2x, 6x, and 7x in length.
2x+6x+7x+195
15x=195
x=195/15=13
the longest side is 7*13=91 meters
Lanuel

The length of the longest side of the triangle is 91 units.

  • Let the unknown length be l.

Given the following data:

  • Perimeter of triangle = 195 meters
  • Ratio = 2:6:7

To find the length of the longest side of the triangle:

Mathematically, the perimeter of a triangle is given by the formula:

[tex]P = A+B+C[/tex]

Where:

  • P is the perimeter.
  • A, B and C are the sides of a triangle.

Substituting the given parameters into the formula, we have;

[tex]195 = 2l + 6l +7l\\\\195 = 15l\\\\l = \frac{195}{15}[/tex]

Length, l = 13 units.

Note: The side with the longest length has the highest ratio (7).

For the longest length:

[tex]7l = 7 \times 13\\\\7l = 91[/tex]

Longest length = 91 units.

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