FAN AND MEDAL TO WHOEVER CAN HELP ME
I need someone to work through this with me and explain it.
A right triangle has base (x - 5) units and height (4x - 10) units.
Part A: What is the square of the length of the hypotenuse of the triangle? Show your work. (4 points)
Part B: What is the area of the triangle? (3 points)
Part C: Using the solution obtained in Part B, explain the closure property of multiplication of polynomials. (3 points)

- anonymous

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- anonymous

me

- anonymous

|dw:1433809231852:dw|
A . you can get the hypotenuse using the pytagorean theorem:
\[H^2=h^2+b^2\]
B . the area can be found as:
\[Area=\frac{b\times h}{2}\]
start with those 2, using the expressions for b and h as a function of x

- anonymous

17x2-90x+125

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## More answers

- anonymous

okay.

- anonymous

Not really. c is just (x-5). So c^2 is (x-5)^2
b is (4x-10) so b^2 is (4x-10)^2

- anonymous

So for the area I would use the squared expressions in the formula or the original?

- anonymous

the original

- anonymous

okay

- anonymous

I am in Algebra I so I haven't taken Geometry yet so I am kinda confused but my teacher gave me this question and I haven't learned how to do this..

- anonymous

ok

- anonymous

for the area you need to use the originals

- anonymous

I'm going to get my sister to help me but thank you!!

- anonymous

ok, just ask here if you need any more help...

- anonymous

@Greg_D my sister wasn't very much help can you still help me?

- anonymous

ill help

- anonymous

okay

- anonymous

what is the question

- anonymous

the same one^

- anonymous

ok

- anonymous

@loveemmmma how far did you get with what @Greg_D suggested?

- anonymous

I got the \[17x ^{2}-90x+125\] = H^2

- anonymous

ok. so for the area multiply the base and height, then multiply by Â½.
\[A=\frac{ 1 }{ 2 }(x-5)(4x-10)\]
Do you know FOIL?

- anonymous

yeah

- anonymous

OK. use it to multiply

- anonymous

sorry, i was away from the computer, i see everything goes fine anyway :)

- anonymous

I'm not sure but I think it might be \[12x ^{2}-5x+25\] I'm really bad at math.. :/

- anonymous

@peachpi @Greg_D is this right??^

- anonymous

|dw:1433812321296:dw|
Divide by 2 to get 2xÂ²-15x+25

- anonymous

oh okay I see what you did.

- anonymous

So that would be the area of the triangle right?

- anonymous

@peachpi ? ^

- anonymous

yes! that would be the area expressed as function of x

- anonymous

amazing explanation @peachpi !!

- anonymous

Okay. But I still need help with part A...

- anonymous

@peachpi @Greg_D part A?

- anonymous

Part A: What is the square of the length of the hypotenuse of the triangle? Show your work. (4 points)

- anonymous

@Greg_D

- anonymous

So what would I do with \[17x ^{2}-90x+125\] that we came up with earlier?

- anonymous

sorry, im not at the computer all the time ...
i took a look at the entire post.. that H^2 was the answer for part A.. is done!

- anonymous

Oh so that is the answer I just leave it like that. and its okay!

- anonymous

yes, that is...

- anonymous

Alright then I think I can answer part C by myself. Thank you so much @Greg_D and @peachpi for your time, patience, and help it means a lot!!

- anonymous

i know you can!
you made an excellent work with parts A and B
keep it up!

- anonymous

Thank you!!

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