The area of a triangle is 6 square feet. The base is 3 times the height.
What is the base of the triangle?
the area is
A = bh/2
3h * h/2 = 6
3h^2 = 12
h^2 = 4
h = 2
b = 3h = 6
check: 2*6/2 = 6
To find the base of the triangle, we first need to find the height using the given information.
Let's assume the height of the triangle as 'h' feet.
According to the given information, the base is 3 times the height, so the base can be expressed as '3h' feet.
The formula to find the area of a triangle is given by:
Area = (base * height) / 2
Substituting the given values, we get:
6 = (3h * h) / 2
Multiplying both sides of the equation by 2 gives us:
12 = 3h^2
Simplifying further gives us:
h^2 = 12/3
h^2 = 4
Taking the square root of both sides, we get:
h = √4
h = 2
Now that we have the height, we can find the base by multiplying it by 3:
base = 3h = 3 * 2 = 6
Therefore, the base of the triangle is 6 feet.
To find the base of the triangle, we need to use the given information that the area is 6 square feet and the base is 3 times the height.
First, let's denote the height of the triangle as 'h' feet.
Since the area of a triangle is given by the formula: Area = (1/2) * base * height, we can write the equation as:
6 = (1/2) * base * h
We also know that the base is 3 times the height, so we can rewrite the equation as:
6 = (1/2) * (3h) * h
Now, let's simplify the equation:
6 = (3/2) * h^2
To solve for 'h', we can multiply both sides of the equation by 2/3:
(2/3) * 6 = h^2
4 = h^2
Taking the square root of both sides of the equation:
√4 = √h^2
2 = h
So, the height of the triangle is 2 feet.
Now, we can find the base of the triangle by multiplying the height by 3:
base = 3 * 2 = 6
Therefore, the base of the triangle is 6 feet.