SOLUTION: How do I find the area of an isosceles triangle whose leg lengths are 8, but the base is unknown ? In advance, thank you.

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Question 402974: How do I find the area of an isosceles triangle whose leg lengths are 8, but the base is unknown ? In advance, thank you.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do I find the area of an isosceles triangle whose leg lengths are 8, but the base is unknown ?
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You don't. That is not enough information.
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you know the height (ie the length that's perpendicular to the unknown base)? If you knew that value, you can easily find half the base (which can be doubled to get the base).


Say that half the base is equal to 'x' and the height is 'h'.


By the pythagorean theorem, we can say x%5E2%2Bh%5E2=8%5E2 or x%5E2%2Bh%5E2=64. Draw a picture so you can see what's going on.


Now solve for x to get x=sqrt%2864-h%5E2%29 (note: we're only considering positive numbers)


Now multiply both sides by 2 to get the length of the entire base 2x=2%2Asqrt%2864-h%5E2%29


So the base is 2%2Asqrt%2864-h%5E2%29 units. From here, just plug in the given height (if there is one) 'h' to evaluate the expression.


Once you've finally figured out the base, you can use that and the height to compute the area.