How do you use Heron's formula to find the area of a triangle with sides of lengths #12 #, #5 #, and #7 #?

Answer 1

The given numbers cannot be lengths of sides of a triangle. (The area is zero)

The Heron's formula says that for any triangle with sides #a,b,c# its area is #A=sqrt(p(p-a)(p-b)(p-c))#, where #p=(a+b+c)/2#

If we substitute given numbers we see, that:

#p=(12+5+7)/2=12#, so
#A=sqrt(12*0*7*5)=0#
You should have noticed, that given numbers cannot be the lengths of sides of a triangle, because #12=7+5# and according to triangle inequalities each side must be smaller then the sum of remaining sides
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Answer 2

To use Heron's formula to find the area of a triangle with side lengths (a), (b), and (c), where (s) is the semi-perimeter calculated as (\frac{a + b + c}{2}):

[Area = \sqrt{s(s - a)(s - b)(s - c)}]

For the given triangle with side lengths (a = 12), (b = 5), and (c = 7):

[s = \frac{12 + 5 + 7}{2} = 12]

[Area = \sqrt{12(12 - 12)(12 - 5)(12 - 7)}]

[Area = \sqrt{12 \times 0 \times 7 \times 5}]

[Area = \sqrt{0}]

[Area = 0]

Therefore, the area of the triangle with side lengths 12, 5, and 7 is 0 square units. This indicates that the given side lengths do not form a valid triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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