A triangle has sides with lengths of 8, 4, and 6. What is the radius of the triangle's inscribed circle?
We can use semiperimeter and Heron's formula
First, we find the semiperimeter, which is the sum of the sides divided by two.
Now, we can use the formula relating inradii, Area, and semiperimeter
And we are done.
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The radius of the triangle's inscribed circle can be found using the formula ( r = \frac{A}{s} ), where ( A ) is the area of the triangle and ( s ) is the semi-perimeter of the triangle. The area ( A ) can be calculated using Heron's formula:
[ A = \sqrt{s(s-a)(s-b)(s-c)} ]
where ( a ), ( b ), and ( c ) are the lengths of the sides of the triangle, and ( s ) is the semi-perimeter calculated as ( s = \frac{a + b + c}{2} ).
For the given triangle with side lengths 8, 4, and 6, the semi-perimeter ( s ) is ( s = \frac{8 + 4 + 6}{2} = 9 ). Using Heron's formula, we can find the area ( A ):
[ A = \sqrt{9(9-8)(9-4)(9-6)} = \sqrt{9 \cdot 1 \cdot 5 \cdot 3} = \sqrt{135} \approx 11.62 ]
Finally, we can calculate the radius of the inscribed circle ( r ):
[ r = \frac{A}{s} = \frac{11.62}{9} \approx 1.29 ]
So, the radius of the triangle's inscribed circle is approximately 1.29.
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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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