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.

Question

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.

Answer 1

Let's assume the height of the triangle to be "h".

According to the given information, the base of the triangle is 6 more than twice the height of the triangle. So, the base will be 2h + 6.

We know that the formula for the area of a triangle is A = (1/2)bh.

Using the given information, we can substitute the values into the formula:

216 = (1/2)(2h + 6)h

Now, we can simplify the equation:

432 = (2h + 6)h

Divide both sides of the equation by 2:

216 = h^2 + 3h

Rearranging the terms, we get:

h^2 + 3h - 216 = 0

We can now factorize this quadratic equation to solve for h:

(h - 9)(h + 24) = 0

So, h can either be 9 or -24. Since height cannot be negative, we discard -24 and take h = 9.

Substituting the value of h into the equation for the base:

base = 2h + 6 = 2(9) + 6 = 18 + 6 = 24

Therefore, the height of the triangle is 9 cm and the base is 24 cm.