Question

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.

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

thats true, but idk what it would be then?

Answer 5

foil the x+7?

Answer 6

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

Answer 7

so the root is -7?

Answer 8

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.

Answer 9

oh I see.how did you do it?

Answer 10

(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

Answer 11

this is what I got

Answer 12

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

Answer 13

so opposite side = 8
adjacent side = 15

Answer 14

is that correct?

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

yes thats it you got it. :)

Answer 20

okay yay! thanks so much for your help :)