the area of a triangle is 27 square feet. its height is three times the length of its base. find the height and base of the triangle. i am unsure of how to set it up, please help

Well, you know that that the area of a triangle

= (1/2)bh, where b is the base and h is the height

but you are told that h = 3b , so

area = (1/2)(b)(3b)
27 = (1/2)(3b^2)
times 2
54 = 3b^2
b^2 = 18
b = √18 or 3√2 ft

base = 3√2 ft and the height is 9√2 ft

check:
area = (1/2)(3√2)(9√2)
= (1/2)(54) = 27

ur mom

yes this is true

4 the anser is 4 gys

To solve this problem, let's first define our variables. We'll let "B" represent the length of the base of the triangle, and "H" represent the height of the triangle.

Given that the area of the triangle is 27 square feet, we can use the formula for the area of a triangle: A = (1/2) * base * height.

Therefore, we have the equation:

27 = (1/2) * B * H

We also know that the height is three times the length of the base, so we can express the height in terms of the base:

H = 3B

Now, we can substitute this value of H into our equation:

27 = (1/2) * B * (3B)

Now, let's simplify the equation:

27 = (1/2) * 3B^2

27 = (3/2) * B^2

To isolate B^2, we can multiply both sides of the equation by 2/3:

(2/3) * 27 = B^2

18 = B^2

Taking the square root of both sides, we find:

B = ±√18

However, since length cannot be negative in this context, we discard the negative solution. Therefore:

B = √18

To find the value of B, we can simplify √18 as follows:

√18 = √(9 * 2) = √9 * √2 = 3√2

So, the length of the base is 3√2.

Since our height "H" is three times the length of the base, we can substitute the value of B into H = 3B:

H = 3 * 3√2 = 9√2

Therefore, the height of the triangle is 9√2 and the base is 3√2.