SOLUTION: A triangular garden has an area of 200ft^2. It's height is 9 ft more than it's base. Find the measure of the base.

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Question 858946: A triangular garden has an area of 200ft^2. It's height is 9 ft more than it's base. Find the measure of the base.
Answer by ben720(159) About Me  (Show Source):
You can put this solution on YOUR website!
Your question was: "A triangular garden has an area of 200ft^2. It's height is 9 ft more than it's base. Find the measure of the base."

let b = x
let h = x+9
A=%281%2F2%29bh
200=%281%2F2%29x%28x%2B9%29
Distribute the x
200=%281%2F2%29%28x%5E2%2B9x%29
Subtract 200 from both sides
0=%281%2F2%29%28x%5E2%2B9x%29-200
Multiply both sides by 2
0=x%5E2%2B9x-400
Plug the values into the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-9+%2B-+sqrt%28+9%5E2-4%2A1%2A-400+%29%29%2F%282%2A1%29+
Do the multiplication
x+=+%28-9+%2B-+sqrt%28+81%2B1600+%29%29%2F2+
x+=+%28-9+%2B-+sqrt%28+1681+%29%29%2F2+
The square root of 1681 is 41.
At this point you have to split it into 2 equations: one where you add 41, and one where you subtract 41. We'll deal with the first one first.
x=%28-9%2B41%29%2F2
x=32%2F2
x=16
Next, deal with Subtract 41
x=%28-9-41%29%2F2
x=%28-50%29%2F2
x=-25
Since the base can't be negative, discard -25.
The base is 16ft.
To check, plug it in to the area formula:
A=%281%2F2%29bh
A=1%2F2%2A16%2A25
A=200
Your checked answer is 16 feet long.