A triangle has sides with lengths of 8, 4, and 3. What is the radius of the triangles inscribed circle?

Answer 1

The triangle does not exist

For any plane triangle with sides a, b, c The following conditions must be satisfied

#a+b>c" "#first condition #a+c>b" "#second condition #b+c>a" "#third condition
If we let #a=8# and #b=4# and #c=3#

The third condition is FALSE !

Therefore , the triangle does not exist ...

God bless...I hope the explanation is useful.

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Answer 2

To find the radius of the inscribed circle in a triangle, you can use the formula:

[ r = \frac{A}{s} ]

Where ( r ) is the radius of the inscribed circle, ( A ) is the area of the triangle, and ( s ) is the semi-perimeter of the triangle. The semi-perimeter ( s ) is calculated as half of the sum of the lengths of the sides of the triangle.

First, calculate the semi-perimeter:

[ s = \frac{8 + 4 + 3}{2} = \frac{15}{2} = 7.5 ]

Next, use Heron's formula to find the area of the triangle. Heron's formula states that for a triangle with sides of lengths ( a ), ( b ), and ( c ), the area ( A ) is given by:

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

Substitute the given side lengths:

[ A = \sqrt{7.5(7.5 - 8)(7.5 - 4)(7.5 - 3)} ]

[ A = \sqrt{7.5 \times (-0.5) \times 3.5 \times 4.5} ]

[ A = \sqrt{7.5 \times 3.5 \times 4.5} ]

[ A = \sqrt{94.5} ]

Now, plug the area and semi-perimeter into the formula for the radius of the inscribed circle:

[ r = \frac{\sqrt{94.5}}{7.5} ]

[ r \approx \frac{9.72}{7.5} ]

[ r \approx 1.296 ]

So, the radius of the triangle's inscribed circle is approximately ( 1.296 ) units.

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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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