Answer:
diameter = m - c
Step-by-step explanation:
In ΔABC, let ∠C be the right angle. The length of the tangents from point C to the inscribed circle are "r", the radius. Then the lengths of tangents from point A are (b-r), and those from point B have length (a-r).
The sum of the lengths of the tangents from points A and B on side "c" is ...
(b-r) +(a-r) = c
(a+b) -2r = c
Now, the problem statement defines the sum of side lengths as ...
a+b = m
and, of course, the diameter (d) is 2r, so we can rewrite the above equation as ...
m -d = c
m - c = d . . . . add d-c
The diameter of the inscribed circle is the difference between the sum of leg lengths and the hypotenuse.
So first you need to open the brackets, so it would be x+2+4x-122=180. Then we can add the 4x and the other x to make 5x, and then by doing 2-122 we get -120. This gives us the equation 5x-120=180. We then isolate the variable by moving the -120 to the other side of the equation and becoming a positive, so it would look like 5x=180+120. Then, we have 5x=300. 300 divides by 5 is 60 making X=60. Hope this helps!
Answer:
- The value of x is 12 units.
Step-by-step explanation:
<u>We know that:</u>
<u>Let's solve using Pythagoras theorem.</u>
- => 13² = 5² + x²
- => 169 = 25 + x²
- => 169 - 25 = x²
- => 144 = x²
- => √x² = √144
- => x = √144
- => x = 12
Hence, the value of x is 12 units.
Answer:.75
Step-by-step explanation:
2x5/18 =.55555
.556 root is .745 the five makes the 4 round up
Answer:
The height is 4.472
Step-by-step explanation:
That formula is Heron's formula.
Where "s" is calculated like this:
s = (a + b + c) / 2
In this case:
a = 14
b = 12
c = 6
replacing:
s = (14 + 12 + 6) / 2
s = 16
Now we calculate the area:
A ^ 2 = 16 * (16−14) * (16−12) * (16−6)
A ^ 2 = 1280
A = 35.777
The area of the triangle is:
A = b * h / 2
In this case we will take the base as the longest side of the triangle, that is to say = 14
Thus:
h = A * 2 / b
h = 35.777 * 2/16
h = 4.472
So the height is 4.472