Answer:
21 cm
Explanation:
We can start by using the formula for the area of a triangle:
Area = (1/2) * base * height
Where the base is b = 24 cm and the height by side a is h = 12 root 3 cm.
Area = (1/2) * 24 cm * 12 root 3 cm = 144 cm^2
We can also use the formula for the area of a triangle in terms of its sides and circumradius:
Area = (abc) / (4R)
Where a, b, and c are the sides of the triangle and R is the radius of its circumcircle.
Plugging in the values we know, we get:
144 cm^2 = (24 cm * a * c) / (4 * 7 root 3 cm)
Simplifying, we get:
9 root 3 cm = a * c / 7
Multiplying both sides by 7 and dividing by a, we get:
c = (63 root 3 cm^2) / a
Substituting the value we know for a, we get:
c = (63 root 3 cm^2) / (12 root 3 cm) = 21 cm
Therefore, the length of side c is 21 cm.
Hopes this helps