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Answer:

Below is the step-by-step explanation.

Step-by-step explanation:

To determine:

Construct a triangle ABC

Information Fetching and Information Steps:

From the given data,

  • [tex]BC\:=\:4\:cm[/tex]
  • [tex]B=60^{\circ }[/tex]
  • [tex]AB+AC=6\:cm[/tex]

Procedure:

  • First draw a line segment [tex]BC\:=\:4\:cm[/tex]
  • Then construct angle of [tex]m[/tex] ∠ [tex]60^{0}[/tex]  at [tex]B[/tex] on [tex]BC[/tex].
  • Taking [tex]B[/tex] as center with [tex]6\:cm[/tex] radius, draw an arc which cuts the ray of  [tex]m[/tex] ∠ [tex]60^{0}[/tex] at [tex]X[/tex].
  • Then Join [tex]X[/tex] and [tex]C[/tex].
  • The draw a perpendicular bisector of [tex]XC[/tex].
  • Wherever this perpendicular bisector intersect [tex]BX[/tex], name that point as [tex]A[/tex]
  • Join [tex]A[/tex] and  [tex]C[/tex].

Thus, ∆ [tex]ABC[/tex] will be a required triangle.

Keywords: triangle, perpendicular bisector, angle

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