SOLUTION: Hi. I am helping my girlfriend do her homework and i just cant seem to figure this one out. We did just fine on all the others...but anyway: If the height of a triangle with a bas

Question 66290: Hi. I am helping my girlfriend do her homework and i just cant seem to figure this one out. We did just fine on all the others...but anyway: If the height of a triangle with a base of 8 inches is tripled, its area is increased by 96 square inches. Find the height of the triangle.
Thank you for your help!!! :)
Found 2 solutions by Nate, stanbon:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Is there a specific triangle?
Lets thinks of a right triangle:
Area = 0.5bh
Before:
b = 8
h = h
Area = 4h
After:
b = 8
h = 3h
Area = 12h
The original triangle's area was increased by 96 square inches after tripling the height.
4h + 96 = 12h
96 = 8h
12 = h
The height before tripling was 12 inches.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If the height of a triangle with a base of 8 inches is tripled, its area is increased by 96 square inches. Find the height of the triangle.
-------
The original area is (1/2)bh
If you triple the height you get
a larger area of (1/2)b(3h)=(3/2)bh
If you subtract the original area from the larger area
you get 96 sq. in as follows:
(3/2)bh-(1/2)bh=96
bh=96
Now, if the base is 8 inches you get:
8h=96
h=12 inches
Cheers,
Stan H.

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