A triangle has an area of 60 in^2. Its base is 10 inches and its height is √x inches. What is the value of x? What is the height of the triangle? Please show all work that you use to determine your answer. (Hint: The formula for the area of a triangle is A= 1/2bh where b=base and h=height)
PLEASE
A = Area = 60 in ^ 2
b = base = 10 in
h = height
A = b h / 2
60 = 10 * h / 2 Multiply both sides by 2
120 = 10 * h Divide both sides by 10
12 = h
h = 12 in
h = sqrt ( x ) Square both sides
h ^ 2 = x
x = h ^ 2 = 12 ^ 2 = 144 in ^ 2
To find the value of x, we need to set up an equation using the area formula for a triangle.
Given that the area of the triangle is 60 in², the base is 10 inches, and the height is √x inches, we can use the formula A = 1/2bh, where A is the area, b is the base, and h is the height.
Substituting the given values, we have:
60 = (1/2)(10)(√x)
To simplify, we can multiply both sides of the equation by 2, resulting in:
120 = 10(√x)
Now, divide both sides of the equation by 10:
12 = √x
To isolate the square root, square both sides of the equation:
12^2 = (√x)^2
Simplifying further:
144 = x
Therefore, the value of x is 144.
To find the height of the triangle, we substitute the value of x back into the original equation:
Height = √x
Height = √144
Height = 12 inches
Thus, the height of the triangle is 12 inches.