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an altitude forms a right angle , right?
2 variables, gonna need 2 equations to figure it out probably
why did you add the u?
broke up the distance y into the two shorter ones u and y-u, they still total y
apply the pythagorean theorem x^2 + u^2 = 12^2 and x^2 + (y + u)^2 = 5^2
now we have 3 variables though, need another equation
would it be x^2+y^2= 12^2 ?
hmm, lets try expanding out the 2 we have from the two small triangles... no y is the total length, cant use that equation
x^2 + u^2 = 144 and x^2 + y^2 + 2*y*u + u^2 = 25
I think the problem is being overcomplicated... partially because of the ambiguity of the wording... The problem only really gives the length of the two sides (5 and 12)... aside from that, we are given a right angle, which appears to be an altitude. We have no other information to infer anything about the shape of the triangle... rearranging equations still leaves us with a variable y in this case... which means the lengths of the sides vary as you change the height, which makes perfect sense... however, it means the height would need to be 0 < y < 5 to have to distinct right triangles and make any sense in regards to the picture. I think the problem wants you to interpret the entire triangle as a right angle... the hilarious thing being that the only right angle they marked would be the one from the altitude... which is really confusing in light of the picture... however, the problem would then be trivial...
the first tells you it is 144 x^2 + u^2 = 144 and y^2 + 2*y*u + 144 = 25
yeah need another info piece
though my previous comment needs an edit... 0 < x < 5
the area of the large triangle is 1/2*y*x heron's relates that to the three sides amd the altitude
the unknowns in that one will be , y and x
For an alternative approach, if anyone is interested: Find the hypotenuse of the larger triangle, whose sides are 5 and 12. The large triangle and the small triange are similar (same angles). Use an equation involving two ratios to determine the unknown height.
lol so the angle at the bottom is right, i guess yeah now reading the directions again and them wanting the total huge length for the large one
that makes it not fun anymore
The "total huge length" for the large one" is the length of the hypotenuse, right? And the sides are 5 and 12. What is the length of this hypotenuse?
Anyone friendly with Pythagoreas?
isn't the equation for that a^2+b^2=c^2
yeah, i did not assume the bottom angle was right
He was the guy who obsessed over right triangles and came up with a very useful theorem. Yes, wintersumtime.
The length of the hypotenuse of the larger triangle is ... ???
i think it may work, using the herem's formula and the two pythagorean theorems, to solve for x,y, and u anyway, not sure
wouldn't it be 13?
Why not take the easiest way out, and then go back and check Heron's Theorem?
Yes, the hyp has length 13. How would u use this fact to determine the unknown height of the larger triangle?
Hint: Apply P's Theorem to the smaller triangle.
And use principles pertaining to similar triangles.
hmm how would you apply it to the smaller triangle though?
Ratios. The smaller triangle has two sides and a hypotenuse. The longer side of the smaller triangle is our unknown. What is the length of the larger side of the larger triangle?
Comparing the hypotenuses of the two triangles, I 'd write a ratio: 5/13. Can you write a ratio that will help y ou find the unknown height and make use of this 5/13?
oh okay, now I see.
So, it seems to me that the correct equation of ratios would be 5/13 = x/12. Agree or disagree?
5 and x pertain to the smaller triangle, whereas 12 and 13 pertain to the larger.
Solve for x.
I got 13x=60 but I don't know how to solve it after that
divide both sides of your equation by 13, to isolate x.
Don't bother to evaluate the resulting fraction; your answer is most accurate if you leave it as the ratio of two integers.
4.6 looks just about right. Is that equal to 60/13?
You could set up another equation of ratios to check that 60/13, but I feel confident that we're on the right track.
This is not to say that the other methods suggested will not work; ours is just simpler.
if not told that the large triangle is right, can it be solved using the diagram i drew for x,y, and u pythagorean for 2 small triangles and heron's (law of cosine)
I don't even remember Heron's Law. If you do, and can understand it, more power to you!
it relates the 3 side lengths to the area