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Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then find its area. (Please answer as soon as possible according to the chapter- Heron's Formula)?
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Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then...
**Solution:**
To find the area of an equilateral triangle, we can use Heron's formula. But before that, let's find the length of each side of the triangle.
Given: x√3 = 48
Dividing both sides of the equation by √3, we get:
x = 48/√3
To rationalize the denominator, we multiply both the numerator and denominator by √3:
x = (48/√3) * (√3/√3)
x = (48√3) / 3
x = 16√3
Now that we have the length of each side of the triangle, we can find its area using Heron's formula.
**Heron's Formula:**
The area (A) of a triangle with side lengths a, b, and c can be calculated using Heron's formula:
A = √(s(s - a)(s - b)(s - c))
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c) / 2
In our case, since the triangle is equilateral, all sides are equal. Let's substitute the values into the formula:
a = b = c = 2x
s = (2x + 2x + 2x) / 2
s = 3x
Now, let's substitute the values of a, b, c, and s into Heron's formula:
A = √(3x(3x - 2x)(3x - 2x)(3x - 2x))
A = √(3x(x)(x)(x))
A = √(27x^4)
A = √(3^3 * (x^2)^2)
A = 3x^2√3
Substituting the value of x from the given equation:
A = 3(48/√3)^2√3
A = 3(48^2/3)√3
A = 3(16^2 * 3)√3
A = 3 * 256 * √3
A = 768√3
Therefore, the area of the equilateral triangle is 768√3 square units.
To find the area of an equilateral triangle, we can use Heron's formula. But before that, let's find the length of each side of the triangle.
Given: x√3 = 48
Dividing both sides of the equation by √3, we get:
x = 48/√3
To rationalize the denominator, we multiply both the numerator and denominator by √3:
x = (48/√3) * (√3/√3)
x = (48√3) / 3
x = 16√3
Now that we have the length of each side of the triangle, we can find its area using Heron's formula.
**Heron's Formula:**
The area (A) of a triangle with side lengths a, b, and c can be calculated using Heron's formula:
A = √(s(s - a)(s - b)(s - c))
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c) / 2
In our case, since the triangle is equilateral, all sides are equal. Let's substitute the values into the formula:
a = b = c = 2x
s = (2x + 2x + 2x) / 2
s = 3x
Now, let's substitute the values of a, b, c, and s into Heron's formula:
A = √(3x(3x - 2x)(3x - 2x)(3x - 2x))
A = √(3x(x)(x)(x))
A = √(27x^4)
A = √(3^3 * (x^2)^2)
A = 3x^2√3
Substituting the value of x from the given equation:
A = 3(48/√3)^2√3
A = 3(48^2/3)√3
A = 3(16^2 * 3)√3
A = 3 * 256 * √3
A = 768√3
Therefore, the area of the equilateral triangle is 768√3 square units.
Community Answer
Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then...
48x as the area of equ. ∆ is √3/4 a^2 and a=2x area= √3/4×4x^2(4and4 cancle) =√3×x×x (√3×x=48 given) 48×x=48x
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Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then find its area. (Please answer as soon as possible according to the chapter- Heron's Formula)?
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Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then find its area. (Please answer as soon as possible according to the chapter- Heron's Formula)? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then find its area. (Please answer as soon as possible according to the chapter- Heron's Formula)? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then find its area. (Please answer as soon as possible according to the chapter- Heron's Formula)?.
Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then find its area. (Please answer as soon as possible according to the chapter- Heron's Formula)? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then find its area. (Please answer as soon as possible according to the chapter- Heron's Formula)? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ques)Each side of an equilateral triangle is 2x cm . If x√3 = 48, then find its area. (Please answer as soon as possible according to the chapter- Heron's Formula)?.
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