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. . .

Given side lengths:
a = 240
b = 133
c = 174

Answer 1

The triangle inequality theorem states that for a triangle to be formed, none of its side should be greater than the sum of the other two sides. The given satisfy this condition. Therefore, a triangle may be formed. 
The area of the triangle is obtained by the Heron's formula,
                         A = sqrt ((s)(s - a)(s - b)(s - c))            ; s = (a + b + c) / 2
Plugging in the values,
  s + (240 + 133 + 174) / 2 = 273.5   
                           A = sqrt ((273.5)(273.5 - 240)(273.5 - 133)(273.5 - 174))j
                               A = 11317.51 unit²

Answer 2

Answer:

The area of triangle formed by given side lengths is 11317.50.

Step-by-step explanation:

A triangle can be formed If the sum of the other 2 sides (except largest side) is longer than the largest side that is a+b>c

Here, given side lengths:

a = 240  

b = 133  

c = 174

Here, largest side is a = 240

so taking sum of other two sides,

b+c = 174+133 = 307 > 240

Hence, triangle can be formed with a, b and c as given lengths.

Calculating area using Heron's formula,

first find the semi perimeter by using given sides,

$\text{s}=\frac{\text{a+b+c}}{2}$

$\text{s}=\frac{\text{240+133+174}}{2}=273.5$

$\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}}$

Substitute values of s, a, b and c in above,

$\text{Area}=\sqrt{273.5(273.5-240)(273.5-133)(273.5-174)}}$

$\text{Area}=\sqrt{273.5 \times 33.5 \times 140.5 \times 99.5}}$

$\text{Area}=\sqrt{128085964.44}$

$\text{Area}=11317.50$(approx)

Thus, the area of triangle formed by given side lengths is 11317.50.