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A median of an equilateral triangle measures 5√3 centimeters. What is the perimeter of the equilateral triangle?​

User Victory
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1 Answer

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Answer: 30 cm

Reason:

The median of a triangle goes from a vertex to the midpoint of the opposite side.

The median of an equilateral triangle will divide the triangle into two congruent 30-60-90 right triangles.

These special types of triangles have the property that:

long leg = shortLeg*sqrt(3)

The median represents the long leg, as it's opposite the 60 degree angle. The short leg must be 5 cm long to fit the template above.

The short leg doubles to 5*2 = 10 cm which is the length of each side of this equilateral triangle.

See the diagram below.

The equilateral triangle has 3 sides of 10 cm each, therefore the perimeter is 3*10 = 30 cm.

A median of an equilateral triangle measures 5√3 centimeters. What is the perimeter-example-1
User Tristan Cunningham
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