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 cm2The 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. Then, according to the given information, the base of the triangle would be (2h + 6).
The formula for the area of a triangle is A = (1/2)bh, where A represents the area, b represents the base, and h represents the height.
Since we know that the area of the triangle is 216 cm^2, we can now set up the equation:
216 = (1/2)(2h + 6)(h)
To solve this equation, let's simplify it:
216 = (h + 3)(h)
Expanding the equation:
216 = h² + 3h
Rearranging the equation to get it in standard quadratic form:
h² + 3h - 216 = 0
Now, we can factor this quadratic equation. The factors of -216 that add up to 3 are 18 and -12:
(h + 18)(h - 12) = 0
Setting each factor equal to zero and solving for h:
h + 18 = 0 or h - 12 = 0
h = -18 or h = 12
Since the height of the triangle cannot be negative, we discard the negative solution:
h = 12 cm
Now, let's substitute this value of h back into the expression for the base:
b = 2h + 6
b = 2(12) + 6
b = 24 + 6
b = 30 cm
Therefore, the length of the base of the triangle is 30 cm and the height is 12 cm.