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If the area of an equilateral triangle is 1003cm², then what is its perimeter?
30 cm
45 cm
60 cm
90 cm
60 cm
Since the area constant is 43, multiply the given area by 4, divide by 3, and take the square root to find a=20. Then, simply multiply by 3 to get the perimeter.
Area of the equilateral triangle = 1003cm²
Area=43a2,Perimeter=3a
Since the area constant is 43, multiply the given area by 4, divide by 3, 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: 1003=43a2.
1003=43a2
Solve for side length a
Cancel 3 from both sides, then multiply by 4 to get a2=400. Taking the square root gives a=20 cm.
a2=400⟹a=20
Calculate perimeter
The perimeter of an equilateral triangle is the sum of its three equal sides: P=3×20=60 cm.
P=3×20=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.
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