The base of a triangle is 8cm greater than the height . The area is 24cm^2. The height is what and the base is what?

area=1/2 bh=1/2 (8+h)h

24=1/2 (8h+h^2)
h^2+8h-48=0
(h+12)(h-4)=0
h=4, b=12

To find the base and height of a triangle, we can use the formula for the area of a triangle:

Area = (base * height) / 2

Given that the area is 24 cm^2, we can substitute this value into the formula:

24 = (base * height) / 2

Since we are given that the base is 8 cm greater than the height, we can express the base as the height plus 8 cm.

Let's denote the height as "h". Therefore, the base can be expressed as "h + 8".

Now we can rewrite the equation substituting the base and height values:

24 = ((h + 8) * h) / 2

We can simplify further by multiplying both sides by 2:

48 = h^2 + 8h

Rearranging the equation, we have:

h^2 + 8h - 48 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's factor the equation:

(h + 12)(h - 4) = 0

Setting each factor to zero, we get two possible values for h:

h + 12 = 0 --> h = -12 (reject as height cannot be negative)
h - 4 = 0 --> h = 4

Therefore, the height of the triangle is 4 cm.

Since the base is 8 cm greater than the height, we can calculate the base:

base = height + 8
base = 4 + 8
base = 12 cm

So, the height of the triangle is 4 cm, and the base is 12 cm.