Question

2x + 6 cm
5(x - 3) cm
Find the length of one side of the equilateral triangle.

Answer 1

side = 20 cm

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

Answer 2

20 cm

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