Question

Answer the question pls i need the answer and i cant find the answer

Answer 1

Equilateral triangles have same sides

• GH=HJ
• 5x-13=11x-61
• 11x-5x=-13+61
• 6x=48
• x=8

Length of each side

• 5(8)-13
• 40-13
• 27

Answer 2

x = 8

measure of each side = 27 units

Explanation:

Properties of an equilateral triangle:

• Regular polygon with 3 sides
• All 3 sides are equal in length
• All 3 interior angles are congruent

If ΔGHJ is an equilateral triangle, the side measures are equal.

`\implies \sf GH = HJ = GJ`

`\implies (5x-13)=(11x-61)=(7x-29)`

To solve for x, choose 2 side lengths, equate them, and solve for x:

`\implies \sf GH=HJ`

`\implies 5x-13=11x-61`

`\implies 5x-13 - 5x =11x-61 - 5x`

`\implies -13=6x-61`

`\implies -13+61=6x-61+61`

`\implies 48=6x`

`\implies 48 / 6=6x / 6`

`\implies x=8`

To find the measure of each side, substitute the found value of x into one of the side expressions:

`\begin{aligned}\implies \textsf{GH}&=5(8)-13\\& =40-13\\& =27\end{aligned}`

Therefore, x = 8 and the measure of each side is 27 units.