Respuesta :

Answer:

side = 20 cm

Step-by-step explanation:

Since the triangle is equilateral then the 3 sides are congruent.

Equate the 2 given sides and solve for x

5(x - 3) = 2x + 6

5x - 15 = 2x + 6 ( subtract 2x from both sides )

3x - 15 = 6 ( add 15 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

then length of side is

2x + 6 = 2(7) + 6 = 14 + 6 = 20 cm

semsee45

Answer:

20 cm

Step-by-step explanation:

Properties of an Equilateral Triangle

  • Regular polygon with 3 sides
  • Sides lengths are equal
  • Interior angles are equal

Given information

  • length of one side:  (2x + 6) cm
  • length of second side:  5(x - 3) cm

Find value of x

As side lengths are equal, equate the expressions and solve for x.

   2x + 6 = 5(x - 3)

⇒ 2x + 6 = 5x - 15

⇒ 2x + 6 + 15 = 5x - 15 + 15

⇒ 2x + 21 = 5x

⇒ 2x + 21 - 2x = 5x - 2x

⇒ 21 = 3x

⇒ 21 ÷ 3 = 3x ÷ 3

⇒ 7 = x

⇒ x = 7

Side lengths

Substitute x = 7 into one of the given expressions.

⇒ length of one side:  2(7) + 6 = 20 cm

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