To find the area of triangle ABC, we can use the fact that the circumcircles of triangles ABX and ACX have the same radius.
Let's denote the radius of the circumcircle as r. Since the circumcircles of triangles ABX and ACX have the same radius, we have the following relationships:
AX * BX * CX = 2 * r^2 * (AX + BX + CX)
13 * 10 * 10 = 2 * r^2 * (13 + 10 + 10)
1300 = 2 * r^2 * 33
r^2 = 1300 / (2 * 33)
r^2 = 19.696969...
Now, let's use Heron's formula to calculate the area of triangle ABC. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semiperimeter of the triangle, given by:
s = (a + b + c) / 2
In this case, the side lengths of triangle ABC are AX, BX, and CX, which are 13, 10, and 10 respectively. Let's calculate the semiperimeter:
s = (13 + 10 + 10) / 2
s = 33 / 2
s = 16.5
Now we can calculate the area using Heron's formula: MyAccountAccess Login
Area = sqrt(16.5 * (16.5 - 13) * (16.5 - 10) * (16.5 - 10))
Area = sqrt(16.5 * 3.5 * 6.5 * 6.5)
Area = sqrt(913.125)
Area ≈ 30.22
Therefore, the area of triangle ABC is approximately 30.22 square units.
To find the number of gallons needed to paint the wall, we need to calculate the total area of the wall in square meters and then convert it to square feet.
The wall is 12 meters tall and 120 meters long, so its total area is:
Area = height × length
= 12 meters × 120 meters
= 1440 square meters
To convert this area to square feet, we can use the conversion factor that 1 square meter is approximately equal to 10.764 square feet: prepaidgiftbalance
Area (in square feet) = Area (in square meters) × 10.764
= 1440 square meters × 10.764
= 15,520.16 square feet
Now, we can calculate the number of gallons needed. We know that 1 gallon covers 150 square feet:
Number of gallons = Total area (in square feet) ÷ Coverage per gallon
= 15,520.16 square feet ÷ 150 square feet
Since we can't buy a fraction of a gallon, we need to round up to the nearest whole number. Therefore, you should buy at least 104 gallons of paint to have enough to cover the entire wall.