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The height of an equilateral triangle is 15 cm. The area of the triangle is
- a)50√3 sq.cm.
- b)70√3 sq.cm.
- c)75√3 sq.cm.
- d)150√3 sq.cm.
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The height of an equilateral triangle is 15 cm. The area of the triang...
We know that each angle in an equilateral triangle is 60°.
So, applying trigonometric formulae in this question we get,
In ΔABD,
tan 60° = AD/BD
⇒ √3 = 15/BD
⇒ BD = 5 √3 cm.
Since, AD is the height of an equilateral triangle; it divides BC into two equal parts, so,
BC = 2 × BD
⇒ BC = 10 √3
Now Area of a Triangle = ½ × Base × Height
⇒ Area = ½ × BC × AD
⇒ Area = ½ × 10 √3 × 15
⇒ Area = 75 √3 cm2
Most Upvoted Answer
The height of an equilateral triangle is 15 cm. The area of the triang...
The formula for the area of an equilateral triangle is A = (sqrt(3)/4) * side^2, where side is the length of one of the sides of the triangle.
Since the triangle is equilateral, all three sides are equal. Let's call the length of one side "x".
We know that the height of the triangle is 15 cm, and since the triangle is equilateral, the height also bisects one of the sides, forming a right triangle with half of one side and the height. Using the Pythagorean theorem, we can solve for x:
x^2 = (15)^2 + (x/2)^2
x^2 = 225 + (x^2)/4
3x^2/4 = 225
x^2 = 300
x = sqrt(300) = 10sqrt(3)
Now that we know the length of one side, we can use the formula for the area of an equilateral triangle:
A = (sqrt(3)/4) * x^2
A = (sqrt(3)/4) * (10sqrt(3))^2
A = (sqrt(3)/4) * 300
A = 75sqrt(3) ≈ 129.9
Therefore, the area of the equilateral triangle is approximately 129.9 square cm.
Since the triangle is equilateral, all three sides are equal. Let's call the length of one side "x".
We know that the height of the triangle is 15 cm, and since the triangle is equilateral, the height also bisects one of the sides, forming a right triangle with half of one side and the height. Using the Pythagorean theorem, we can solve for x:
x^2 = (15)^2 + (x/2)^2
x^2 = 225 + (x^2)/4
3x^2/4 = 225
x^2 = 300
x = sqrt(300) = 10sqrt(3)
Now that we know the length of one side, we can use the formula for the area of an equilateral triangle:
A = (sqrt(3)/4) * x^2
A = (sqrt(3)/4) * (10sqrt(3))^2
A = (sqrt(3)/4) * 300
A = 75sqrt(3) ≈ 129.9
Therefore, the area of the equilateral triangle is approximately 129.9 square cm.
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The height of an equilateral triangle is 15 cm. The area of the triangle isa)50√3 sq.cm.b)70√3 sq.cm.c)75√3 sq.cm.d)150√3 sq.cm.Correct answer is option 'C'. Can you explain this answer?
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