Question 7207: the hypotenuse of a right triangle is 26 feet long. one leg of the triangle is 14 feet longer than the other leg. find the lengths of the legs of the triangle. please, and thank you!!
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! 2 classic right-angled triangles are the 3,4,5 and the 5,12,13
Taking the second example and just scaling it up...10,24,26
look at the numbers you have....26 for the hypotenuse and the other two have one being 14 larger than the other...voila that is your answer.
Doing it through maths.
let one side = x.
Other side is therefore x+14
so, 
so factorise it! The 2 factors are, hopefully, one of the following possibilities:
1x480
2x240
3x160
4x120
5x96
6x80
8x60
10x48
12x40
15x32
16x30
20x24
For one of these pairs of factors, one number must be multiplied by 2 and then added/subtacted to the other factor to give 18
How about 10x48?...2x10 is 20. 20 and 48 differ by 28. So, (2x + 40)(x - 10) = 0
so, 2x+40 = 0 or x-10 = 0
so x=-20 or x=10.
Since we are dealing with lengths, -20 makes no sense, so x must be 10.
Looking at my definition, the other length must therefore be 14 greater...24.
So we have a 10,24,26 triangle, which is exactly what i got by just knowing a few basic things about Right angled triangles.
jon.
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