An equilateral triangle and a regular hexagon have the same perimeter. If a side of the hexagon is 15 cm, what is the altitudeof the equilateral triangle?
Answer: 15 square root of 3 cm
But I don't know the solution/formula, please help
Answers
Answer:
15 ✓ 3 cm
Step-by-step explanation:
A regular hexagon has 6 sides, all of which are equal.
Therefore, perimeter of the hexagon = 15 × 6 = 90 cm
Let the side of the equilateral triangle be S.
Since hexagon and the triangle have equal perimeter,
3S = 90 and thus, S = 30 cm
Now, height of an equilateral triangle is given by [ ( √3 ) / 2 } × S ]
Thus, height of given equilateral triangle
= [ { ( √3 ) / 2 } × 30 ]
= 15 √ 3 cm
Step-by-step explanation:
No. of sides of regular hexagon = 6
So it's perimeter = 15*6 = 90 cm
Now given that peri(triangle) = peri(hexagon)
3x = 90
Side of equilateral triangle = 30cm
Altitude of equilateral triangle is given by formula = √3*side/2
= √3 * 30 /2
= 15√3 cm
Above image is the proof for altitude of equilateral triangle
= √3side/2
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