Question

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 = 127
c = 281

Help me please

Answer 1

Answer on Question #42443 – Math - Geometry

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 = 127

c = 281

Help me please

Solution:

If the sum of the other 2 sides (without longest side) is not longer than the longest side then it can not form a triangle:

$$\begin{array}{l} a + b > c; \\ 240 + 127 > 281 \\ 367 > 281 \\ \end{array}$$

Hence, lengths $a$, $b$ and $c$ can form a triangle.

Heron's formula to find the area of the triangle. $\left(s = \frac{a + b + c}{2} = \frac{240 + 127 + 281}{2} = 324 - \text{half of the triangles perimeter}\right)$:

$$A = \sqrt{\frac{s(s - a)(s - b)(s - c)}{15183.8}} = \sqrt{\frac{324 \cdot (324 - 240)(324 - 127)(324 - 281)}{15183.8}} = 15183.8$$

Answer: lengths $a$, $b$ and $c$ can form a triangle, area of the triangle is equal to 15183.8

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