Answer:
base = 8 cm
height = 12 cm
Step-by-step explanation:
We will need the formula for area of a trianlge, which is
A = (1/2)bh where b is the base, and h is the height
We are given two formulas...
"The height of a triangle is 8 centimeters greater than half its base" becomes
h = (1/2)b + 8
"The area of the triangle is 48 square centimeters" becomes
48 = (1/2)bh
Plug the first formula into the second to solve for h
48 = (1/2)b[(1/2) + 8] (h becomes (1/2)b + 8)
Now solve for b
48 = (1/4)b² + 4b
**This is a quadratic euquation. Solve using factoring...
(1/4)b² + 4b - 48 = 0 (subtract 48 from both sides)
b² + 16b - 192 = 0 (multiply by 4 so b² is by itself, it's easier to factor this way)
Now factor...
(b + 24)(b - 8) = 0 (you need two numbers that add to 16 and multiply to -192)
Set each binomial equal to zero and solve for b
b + 24 = 0
b = -24
**this anwser is not valid because b is a length, and you can't have negative length
b - 8 = 0
b = 8
Since the other solution is invalid, the base is b
If the base is b, then the height is...
h = (1/2)b + 8
h = (1/2)(8) + 8
h = 4 + 8
h = 12
