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

Answer the question pls i need the answer and i cant find the answer-example-1
User DannyLane
by
6.4k points

2 Answers

10 votes

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
User Suz
by
6.8k points
5 votes

Answer:

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.

User Dienekes
by
6.7k points
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