The formula for the area of a triangle is 𝐴𝑟𝑒𝑎 = 1/2𝑏ℎ, where b represents the base of the
triangle and h represents the height of the rectangle. A triangle has an area of 216 cm2. The base of the triangle is 6 more than twice the height of the triangle. Find the length of the base and height.
Let's represent the height of the triangle as h.
According to the given information, the base of the triangle is 6 more than twice the height:
base = 2h + 6
The formula for area of a triangle is A = 1/2 * base * height:
216 = 1/2 * (2h + 6) * h
Let's simplify this equation:
216 = h * (2h + 6) / 2
216 * 2 = h * (2h + 6)
432 = 2h^2 + 6h
2h^2 + 6h - 432 = 0
Now we can solve this quadratic equation. Let's factor it:
(2h - 18)(h + 24) = 0
Setting each factor to zero, we get two possible solutions:
2h - 18 = 0 -> 2h = 18 -> h = 9
h + 24 = 0 -> h = -24
Since the height of the triangle can't be negative, we discard the second solution.
So, the height of the triangle is 9 cm.
Using this value, we can find the length of the base:
base = 2h + 6 = 2 * 9 + 6 = 18 + 6 = 24
Therefore, the length of the base is 24 cm and the height is 9 cm.