How do you use Heron's formula to find the area of a triangle with sides of lengths #18 #, #7 #, and #19 #?
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To use Heron's formula to find the area of a triangle with sides of lengths (a), (b), and (c), where (s) is the semi-perimeter of the triangle (defined as (s = \frac{a + b + c}{2})), follow these steps:
- Calculate the semi-perimeter (s) using the formula (s = \frac{a + b + c}{2}).
- Use Heron's formula: Area ((A)) = (\sqrt{s(s - a)(s - b)(s - c)}).
- Substitute the values of (a), (b), and (c) into the formula.
Given the side lengths (a = 18), (b = 7), and (c = 19):
- Calculate the semi-perimeter (s) as (s = \frac{18 + 7 + 19}{2} = \frac{44}{2} = 22).
- Use Heron's formula: (A = \sqrt{22(22 - 18)(22 - 7)(22 - 19)}).
- Perform the calculation:
[ A = \sqrt{22(22 - 18)(22 - 7)(22 - 19)} ] [ A = \sqrt{22(4)(15)(3)} ] [ A = \sqrt{22 \times 4 \times 15 \times 3} ] [ A = \sqrt{3960} ]
So, the area of the triangle is (A = \sqrt{3960}).
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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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