Answer :
The height of the triangle, we can use the formula for the area of a triangle. The correct answer is option d i.e. 6.2 inch. The formula for the area of a triangle is A = (1/2) * base * height.
In this case, side c is the base and the altitude to side c is the height. We are given that side c has a length of 6 inches and the altitude to side c has a length of x inches.
The area of the triangle can also be calculated using Heron's formula, which states that the area of a triangle can be found using the lengths of its sides. Heron's formula is given by
A = sqrt(s * (s - a) * (s - b) * (s - c)), where s is the semi perimeter of the triangle and is calculated as s = (a + b + c) / 2.
In this case, we can calculate the semiperimeter as s = (9 + 9 + 6) / 2 = 12.
Using Heron's formula, we can find the area of the triangle as A = sqrt(12 * (12 - 9) * (12 - 9) * (12 - 6)) = sqrt(12 * 3 * 3 * 6) = sqrt(648).
Now, we can equate the two formulas for the area of the triangle:
(1/2) * 6 * x = sqrt(648)
Simplifying the equation:
3x = sqrt(648)
Squaring both sides of the equation:
9x^2 = 648
Dividing both sides by 9:
x^2 = 72
Taking the square root of both sides:
x = sqrt(72)
Simplifying:
x = sqrt(36 * 2)
x = sqrt(36) * sqrt(2)
x = 6 * sqrt(2)
Therefore, the height of the triangle is 6 * sqrt(2) inches.
To know more about Area Of A Triangle visit:
https://brainly.com/question/29156501
#SPJ11
