SOLUTION: Find are of Triangle STU. It is a right triangle, I don't know how to do that on here. But the 'height' is missing, the hypotenuse is 12, and the base is 4. I did a^2 + 4^2 = 12^2

Algebra ->  Triangles -> SOLUTION: Find are of Triangle STU. It is a right triangle, I don't know how to do that on here. But the 'height' is missing, the hypotenuse is 12, and the base is 4. I did a^2 + 4^2 = 12^2       Log On


   



Question 810599: Find are of Triangle STU. It is a right triangle, I don't know how to do that on here. But the 'height' is missing, the hypotenuse is 12, and the base is 4. I did a^2 + 4^2 = 12^2 and get a^2 + 16=144
So 144-16=128
a^2=128
+sqrt+%28+128+%29+ is +sqrt+%2864%2A2%29+ which is 8+sqrt+%28+2+%29+. But 8*4 +sqrt+%28+2%29+ is 32 +sqrt+%28+2+%29+ and the answer key says it's 16 +sqrt+%28+2+%29+

Found 2 solutions by Okeke_Christian, MathLover1:
Answer by Okeke_Christian(26) About Me  (Show Source):
You can put this solution on YOUR website!
You may be using the formula to solve directly, and that's why the calculator is giving you the answer.
Don't forget my dear, the area of a right-angled triangle is 1/2(b x h), not b x h.
Did I get where the problem is coming from?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the hypotenuse is 12, and the base is 4
you did a%5E2+%2B+4%5E2+=+12%5E2....this is correct
and you get a%5E2+%2B+16=144....also correct
now move 16 to the right side
a%5E2+=144-16
a%5E2+=128....find a
a++=sqrt%28128%29
a++=sqrt%282%2A64%29
a++=sqrt%282%2A8%5E2%29
highlight%28a++=8sqrt%282%29%29.....exact solution
you can find approximate value
a++=8%2A1.4142135623730950488016887242097
a++=11.313708498984760390413509793678..round it
a++=11.314

if the answer key says it's 16 +sqrt+%28+2+%29+, that is not correct; check and see
%2816sqrt+%28+2+%29%29%5E2+%2B+16=144
16%5E2%2A2+%2B+16=144
256%2A2+%2B+16=144
512+%2B+16=144
528%3C%3E144
let's check our solution

%288sqrt+%28+2+%29%29%5E2+%2B+16=144
8%5E2%2A2+%2B+16=144
64%2A2+%2B+16=144
128+%2B+16=144
144=144