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If the area of an equilateral triangle is 1003тАЛcm┬▓, then what is its perimeter?
30 cm
45 cm
60 cm
90 cm
60 cm
Since the area constant is 43тАЛтАЛ, multiply the given area by 4, divide by 3тАЛ, and take the square root to find a=20. Then, simply multiply by 3 to get the perimeter.
Area of the equilateral triangle = 1003тАЛcm┬▓
Area=43тАЛтАЛa2,Perimeter=3a
Since the area constant is 43тАЛтАЛ, multiply the given area by 4, divide by 3тАЛ, and take the square root to find a=20. Then, simply multiply by 3 to get the perimeter.
Students often forget to multiply by 4 or miscalculate the square root of 400, leading to an incorrect side length a.
Equate area to formula
Start by setting the area formula equal to the given value: 1003тАЛ=43тАЛтАЛa2.
1003тАЛ=43тАЛтАЛa2
Solve for side length a
Cancel 3тАЛ from both sides, then multiply by 4 to get a2=400. Taking the square root gives a=20 cm.
a2=400тЯ╣a=20
Calculate perimeter
The perimeter of an equilateral triangle is the sum of its three equal sides: P=3├Ч20=60 cm.
P=3├Ч20=60
C is correct because the calculated side length is 20 cm, resulting in a perimeter of 60 cm.
This is a fundamental skill for coordinate geometry problems involving equilateral triangles, where you might need the side length to find the height or vertices.