RIGHT TRIANGLE... opposite=2x, adjacent=x+1, and hypotenuse=x+19...find x

THA ANSWERS SUPPOSED TO BE 15 BUT IDK HOW TO GET THERE. :'(

Question

RIGHT TRIANGLE... opposite=2x, adjacent=x+1, and hypotenuse=x+19...find x

THA ANSWERS SUPPOSED TO BE 15 BUT IDK HOW TO GET THERE. :'(

jdoe0001 · Answer

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jdoe0001 · Answer

hmm... so how do you know is .. .15 though?

jdoe0001 · Answer

ohh.. you saw it on the back of the book... I see

anonymous · Answer

WELL YEAH, KINDA...THE ETACHER GAVE US THE ANSWERS...BUT YOU HAVE TO SHOW WORK, *oops it was on upper case

anonymous · Answer

youre supposed to factor using the pythagorean theorem

jdoe0001 · Answer

soo... ok... how far down have you tried?

anonymous · Answer

so far i have -13x=square root of 180

anonymous · Answer

but idk if thats right

anonymous · Answer

By the pythagorean theorem:

(2x)^2 + (x+1)^2 = (x+19)^2

=> 4x^2 + x^2 + 2x + 1 = x^2 + 38x + 361

=> 4x^2 - 36x - 360 = 0  --> factor out 4

=> x^2 - 9x - 90 = 0 

=> (x-15)(x+6) = 0

=> x = 15 or x = -6

Since 'x' has to be a positive number because it's involved in the lengths of the sides of the triangles which means that we can discard the solution x = -6.

Therefore x = 15.

@merylzac