# A triangle has sides with lengths of 5, 1, and 3. What is the radius of the triangles inscribed circle?

The given triangle is not possible to be formed.

In any triangle the sum of any two sides must be greater than the third side.

Since, the property of triangle is not verified therefore, there exists no such triangle.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the radius of a triangle's inscribed circle, 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 (half of the perimeter).

First, calculate the semi-perimeter ( s ):

[ s = \frac{a + b + c}{2} ] [ s = \frac{5 + 1 + 3}{2} = 4.5 ]

Next, use Heron's formula to find the area ( A ) of the triangle:

[ A = \sqrt{s(s - a)(s - b)(s - c)} ] [ A = \sqrt{4.5(4.5 - 5)(4.5 - 1)(4.5 - 3)} ] [ A = \sqrt{4.5(-0.5)(3.5)(1.5)} ] [ A = \sqrt{4.5(-0.4375)(1.5)} ] [ A = \sqrt{-2.4375} ] [ A \approx 1.56 ]

Now, substitute the values of ( A ) and ( s ) into the formula for the radius of the inscribed circle:

[ r = \frac{1.56}{4.5} ] [ r \approx 0.3467 ]

So, the radius of the triangle's inscribed circle is approximately 0.3467 units.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- Points #(2 ,5 )# and #(3 ,4 )# are #( pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
- A triangle has corners at #(9 ,8 )#, #(2 ,3 )#, and #(1 ,4 )#. What is the area of the triangle's circumscribed circle?
- What is the measure of angle a?
- A triangle has corners at #(4 , 5 )#, #(1 ,3 )#, and #(3 ,4 )#. What is the radius of the triangle's inscribed circle?
- What is the center, radius, and intercepts of the circle # (x-3)^2+(y+7)^2 = 16#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7