How do you use Heron's formula to find the area of a triangle with sides of lengths #2 #, #5 #, and #5 #?

Question

How do you use Heron's formula to find the area of a triangle with sides of lengths #2  #, #5    #, and #5   #?

Allison Allen · Accepted Answer

#2sqrt6#

Use the Heron's formula

#color(blue)(sqrt(s(s-a)(s-b)(s-c))#

Where

#color(red)(a,b,c=sides,s=(a+b+c)/(2)#

#s# is also defined as the Semi-perimeter of the #triangle#

Values

#color(orange)(a=2#

#color(orange)(b=5#

#color(orange)(c=5#

#color(orange)(s=(2+5+5)/2=12/2=6#

Start to solve it

#rarrsqrt(6(6-2)(6-5)(6-5))#

#rarrsqrt(6(4)(1)(1))#

#rarrsqrt(6(4))#

#color(green)(rArrsqrt(24)=sqrt(4*6)=2sqrt6~~4.899#

Jayden Jackson · Answer

undefined To use Heron's formula to find the area of a triangle with sides of lengths 2, 5, and 5, you first need to calculate the semiperimeter ($s$) of the triangle. Then, you can use Heron's formula, which states that the area ($A$) of a triangle with side lengths $a$, $b$, and $c$ is given by:

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

where $s$ is the semiperimeter, and $a$, $b$, and $c$ are the lengths of the sides.

For the given triangle with side lengths 2, 5, and 5:

1. Calculate the semiperimeter, $s$, using the formula: $s = \frac{a + b + c}{2}$.
2. Substitute the side lengths into Heron's formula to find the area, $A$.

Let's calculate:

1. $ s = \frac{2 + 5 + 5}{2} = \frac{12}{2} = 6 $

2. $ A = \sqrt{6(6-2)(6-5)(6-5)} = \sqrt{6(4)(1)(1)} = \sqrt{24} $

Therefore, the area of the triangle is $ \sqrt{24} $ square units.