Question

An equilateral triangle has a side length of 1.4x + 2 inches

. A regular hexagon has
a side length of 0.5x + 2 inches. The perimeters are equal. What is the side length
of the triangle? What is the side length of the hexagon? Show your work.
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SOLUTION

Answer 1

The Perimeter of an equilateral triangle = 1.4x+2+1.4x+2+1.4x+2

= 4.2x+6

The Perimeter of a regular hexagon = 0.5x+2+0.5x+2+0.5x+2+0.5x+2+0.5x+2+0.5x+2

= 3x+12

Given that the perimeters are equal

4.2x+6 = 3x+12

4.2x - 3x = 12-6

1.2x = 6

x = 6/1.2

x=5

The side length of the triangle = 1.4x+2

= 1.4 (5) +2

= 9 inches

The side length of hexagon = 0.5x+2

= 0.5(5) +2

= 4.5inches