Question

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Answer 1

Here,

AC ≅ AB

→ 5x -6 = 3x+8

→ 5x - 3x = 8+6

→ 2x = 14

→ x = 14/2

→ x = 7

Now Putting the value of x

AC = 5x - 6

= 5(7) -6

= 35 -6

= 29

AB = 3x + 8

= 3(7) +8

= 21 + 8

= 29

BC = 2x + 15

=2(7)+15

= 14 + 15

= 29

Thus,

• Side length of equilateral triangle is 29.

More Information

Area of triangle

`\sf \: (1)/(2)bh`

Area of equilateral triangle

`\sf \: ( √(3) )/(4) {a}^(2)`

Area of Isosceles Triangle

`\sf \: (b)/(4) \sqrt{ {4a}^(2) - {b}^(2) }`

Answer 2

Side length of equilateral triangle is = 29 units

Step-by-step explanation:-

In geometry, an equilateral triangle is a triangle that has all its sides equal in length.

3 given lengths are

3x+8 , 5x - 6 , 2x +15

so,

`\rm \: 3x + 8 = 5x - 6 = 2x + 15`

consider 2 sides,

`\rm \implies 3x + 8 = 2x + 15`

`\rm \implies 3x - 2x = 15 - 8`

`\rm \implies x= 7`

so,

`\rm \: 3x + 8 = 3 * 7 + 8 = 29`

As equilateral triangle

3x+8 = 5x - 6 = 2x +15 = 29

The sides of a triangle are straight lines that are joined by the three vertices of the triangle.

so,

Side,length of equilateral triangle is 29 units

Note :-

Number of Sides = 3

Number of angles = 3

Each interior angle = 60

Each exterior angle = 120

Perimeter = 3 times of side-length

Area = √3/ 4 x (side)2

Height = √3 (side)/2