- anonymous

Hello, I need help sloving a pythagorean problem. The side of the triangle is 5m,3m, and 2m+6

- schrodinger

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- anonymous

the formula is a^2+b^2=c^2

- anonymous

Which one is the hypotnus? the longest side?

- anonymous

yes

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## More answers

- anonymous

rigth i'm using that formula but my answers are coming up negative? :-(

- anonymous

are you trying to solve for m?

- anonymous

no romero

- anonymous

yes slove for m

- anonymous

ok

- anonymous

i got negative 5 and 1 and then i time them numbers by the giving number and they are still negative

- anonymous

\[(5m) + (3m)^2 = (2m+ 6)^2\]

- anonymous

woops forgot a squared

- anonymous

(5m)^2 + (3m)^2 = (2m + 6)^2
m = -0.76619 or m = 1.56619
But m = -0.76619 is an extraneous solution, so m = 1.56619
Consequently, the sides are about 7.83, 4.70, and 9.13

- anonymous

\[(5m)^2 + (3m)^2 = (2m+6)^2\]

- anonymous

Romero correct....dinosaur that looks correct how you come up with that answer?

- anonymous

You have a quadratic so you can have two values for m

- anonymous

if square all the numbers you get\[25^2 + 9m^2= 4m^2 + 24m+ 36\]
get everything to one side you have
\[30m^2 - 24m -36 = 0\]

- anonymous

where a = 30 b =-24 c=-36 and you use the quadratic formula to find the answers. Do you know to do from now on?

- anonymous

Romero that is what i got too and at the end the number are not coming out as whole numbers

- anonymous

Does the question say anything about what side is the longest? or m belongs to some interval?

- anonymous

the picture shows 5m to be the longest side

- anonymous

I see!

- anonymous

lol wow then we have it wrong

- anonymous

I thought so, because that would make the answer look nicer :)

- anonymous

if 5m is the longest side, then:
\[(5m)^2=(3m)^2+(2m+6)^2 \implies 25m^2=9m^2+4m^2+24m+36\]
\[\implies 12m^2-24m-36=0 \implies m^2-2m-3=0\]
then after factorization:
\[(m-3)(m+1)=0 \implies m=3, m=-1\]

- anonymous

since the value of m represents length, we only take the positive value, that's m=3.

- anonymous

awww thanks that look like that might be answer your a lifesaver :-)

- anonymous

then your sides are:
5m=15, 3m=9 and 2m+6=12

- anonymous

You're welcome :)

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