what is the base and heigt of a triangle that has an area of 27 feet squared and the height is 3x base?
First let's look at the formula to find the area of a triangle.
Area = (base x height)/2
Now, the question tells us that the height is 3x the base. Therefore, it is safe to say that if B is the base then the height must be 3B. We can then re-write the formula:
27 = ( B x 3B)/2
Can you solve from there?
When you solve the equation above, you'll get a value for the base of the triangle. Simply multiple that value by 3 in order to get the height.
To find the base and height of the triangle, given the area and the relationship between the height and base, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Let's substitute the known values into the formula:
27 = (1/2) * base * (3x base)
Now, let's simplify the equation:
27 = (3/2) * x * base^2
To isolate the base^2 term, divide both sides of the equation by (3/2) * x:
27 / ((3/2) * x) = base^2
Simplifying further:
18 / x = base^2
Take the square root of both sides to solve for the base:
√(18 / x) = base
Therefore, the base of the triangle is √(18 / x).
We are also given that the height is 3x times the base. So, the height can be expressed as:
height = 3x * √(18 / x)
Simplifying further:
height = 3√(18x)
Hence, the base of the triangle is √(18 / x) and the height is 3√(18x).