The perimeters of the triangles shown below are equal
2 answers:
Answer:
Step-by-step explanation:
The perimeter of a shape is the sum of all of its side lengths. Therefore, the perimeter of the first triangle is and the perimeter of the second triangle is
.
We are given that the perimeters of the triangles are equal, so equals
. As an equation, that would be
. Solving for
, we get:
(Add
to both sides of the equation to isolate
)
(Divide both sides of the equation by
to get rid of
's coefficient)
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Answer:
r =
Step-by-step explanation:
So we need to complete the square for both parts of the equation
First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6
So first we can complete the square for x² + 2x
To do so we need to use to figure out the number we need to add to both sides
In this case our b is 2, so substituting this in we get
Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1
Now we can follow the same steps to complete the square for y² + 4y
Here our b is 4, so substituting this in we get
Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4
Now condensing everything we have (x + 1)² + (y + 2)² = 11
The formula for a circle is (x - h)² + (y - k)² = r²
In our equation we have r² = 11
To find the radius we need to take the square root of both sides to get r =