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Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 240 b = 132 c = 330

Respuesta :

Ashraf82

Answer:

a, b, and c can be formed a triangle

The area of the triangle is 13385.87 square units.

Step-by-step explanation:

Let us revise an important fact in any triangle

  • The sum of the lengths of the two shortest side must be greater than the length of the longest side

The length of the sides are a = 240, b = 132, and c = 330

∵ The two shortest sides are a = 240 and b = 132

∵ a + b = 240 + 132 = 372

∵ The longest side is c = 330

∵ 372 > 330

∴ a + b > c

∴ a, b, and c can be formed a triangle

Let us revise the Heron's formula of the area of the triangle

  • Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex], where a, b,c are the lengths of the sides of the triangle, and [tex]p=\frac{a+b+c}{2}[/tex]

∵ [tex]p=\frac{240+132+330}{2}=351[/tex]

∴ [tex]Area = \sqrt{351(351-240)(351-132)(351-330)}[/tex]

∴ [tex]Area = \sqrt{351(111)(219)(21)}[/tex]

∴ [tex]Area=13385.87[/tex]

The area of the triangle is 13385.87 square units.

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