## laylam25 2 years ago Find the lengths of the missing sides of the triangle: 17 on the hypotnuse, x+7 on the adjacent side, and x on the opposite side.

1. MarcLeclair

(x+7)^2 + x^2= 17^2. You can solve it yourself?

2. laylam25

are you sure we use a^2+b^2=c^2?

3. MarcLeclair

Yes, the hypothenuse is the longest side of a right angle triangle. Unless I forgot my basic geometry.

4. laylam25

thats true, but idk what it would be then?

5. laylam25

foil the x+7?

6. MarcLeclair

yes, simplify the x+7, you will get a quadratic, either find its root by factoring or use the quadratic formula

7. laylam25

so the root is -7?

8. MarcLeclair

it can't be a negative. I got 6. ( I did it really quickly so you,d have to check). But a measurement cannot be negatie. ever.

9. laylam25

oh I see.how did you do it?

10. MarcLeclair

(x+7)(x+7) + x^2 = 17^2. Bring all to one side it will give you 2(x^2+14x-120). One of your zero will b -20 the other will be 6

11. laylam25

this is what I got

12. laylam25

17^2 = [x+7]^2 + x^2 289 = x^2 + 14x + 49 + x^2 2x^2 + 14x - 240 = 0 divide by 2 x^2 + 7x - 120 = 0 factor [x + 15][x - 8] = 0

13. laylam25

so opposite side = 8 adjacent side = 15

14. laylam25

is that correct?

15. MarcLeclair

yes that should be it, if what I calculated is right.

16. MarcLeclair

oh wait wait, with yoru calculations you get x= 8, you have to plug it in x+7 therefore 8+7 = 15. Don't forget you had an initial equation

17. laylam25

yeah x=8 because when I set x+15=0 I get a negative 15. so I plug 8 back into x+7?

18. laylam25

so my opposite side is just 8? and adjacent is 15?

19. MarcLeclair

yes thats it you got it. :)

20. laylam25

okay yay! thanks so much for your help :)