The base of a triangle is 10 cm longer than the height. Determine the height of the triangle if its area is 48 cm^2.
-I just plugged in number and got 6cm for the height and 16cm for the base. But I need to show work and I cant remember how to solve this.
The height h is b - 10
(1/2) b (b-10) = 48
b^2 -10b = 96
(b-16)*(b+6) = 0
b = 16. h = b-10 = 6
The other root (b = -6) makes no sense.
The triangle area is A = bh/2 where b = the base and h = the height.
Therefore, A = (h + 6)h/2 = 24. I imagine you can take it from here.
To determine the height of the triangle, we can set up an equation using the formula for the area of a triangle:
Area of a triangle = (base * height) / 2
Given that the area is 48 cm^2, we have:
48 = (base * height) / 2
Now, we also know that the base of the triangle is 10 cm longer than the height. So we can express the base in terms of the height:
base = height + 10
Substituting this value into the equation, we have:
48 = ((height + 10) * height) / 2
To solve for the height, we can multiply both sides of the equation by 2:
2 * 48 = (height + 10) * height
Simplifying further:
96 = height^2 + 10 * height
Rearranging the equation and setting it equal to zero:
height^2 + 10 * height - 96 = 0
Now, we can factor this quadratic equation:
(height + 16) * (height - 6) = 0
Solving for the height gives us two possible solutions: height = -16 or height = 6. Since height cannot be negative in this context, we discard the negative value.
Therefore, the height of the triangle is 6 cm.