laylam25
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.



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

laylam25
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are you sure we use a^2+b^2=c^2?

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

laylam25
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thats true, but idk what it would be then?

laylam25
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foil the x+7?

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

laylam25
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so the root is 7?

MarcLeclair
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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.

laylam25
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oh I see.how did you do it?

MarcLeclair
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(x+7)(x+7) + x^2 = 17^2.
Bring all to one side
it will give you 2(x^2+14x120).
One of your zero will b 20 the other will be 6

laylam25
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this is what I got

laylam25
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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

laylam25
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so opposite side = 8
adjacent side = 15

laylam25
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is that correct?

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

MarcLeclair
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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

laylam25
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yeah x=8 because when I set x+15=0 I get a negative 15. so I plug 8 back into x+7?

laylam25
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so my opposite side is just 8? and adjacent is 15?

MarcLeclair
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yes thats it you got it. :)

laylam25
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okay yay! thanks so much for your help :)