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.