the length of one leg of a right triangle is 9ft. The length of the hypotenuse is 3ft longer than the other leg. Find the length of the hypotenuse and the other leg.

Question

anonymous · Answer

$$n^2 + 9^2 = (n+3)^2$$

anonymous · Answer

which gives me?

anonymous · Answer

The answer that you will have to figure out! :D

anonymous · Answer

im looking for the length of the hypotenuse and the other leg and this is my first time doing this. Can you please walk me through this once?

anonymous · Answer

Ok. Do you remember the Pythagorean theorem?

anonymous · Answer

a^2+b^2=c^2 yes

anonymous · Answer

Ok. That's the basis of what I wrote above. Since one leg was given, and the hypotenuse was expressed in terms of the other leg.

anonymous · Answer

Do you know how to expand $(n+3)^{2}$?

anonymous · Answer

not really :/

anonymous · Answer

There is a formula but I never remember it. You can just FOIL, though.

anonymous · Answer

n^2+3^2?

anonymous · Answer

You forgot the middle terms. $(a + b)(c + d) = ab + ad + bc + bd$

anonymous · Answer

ah ok.

anonymous · Answer

Er... ac + ad + bc + bd... sorry.

anonymous · Answer

no worries im listening

anonymous · Answer

So $(n + 3)(n + 3) = n^2 + 3n + 3n + 9$

anonymous · Answer

So far we have $n^2 + 81 = n^2 + 6n + 9$

anonymous · Answer

correct

anonymous · Answer

Good news, we don't have to solve a quadratic equation, because we can just subtract the $n^2$, it should be easy to solve then.

anonymous · Answer

so the length of the hypotenuse is?

anonymous · Answer

Slow down! I'm walking you through it. :P

anonymous · Answer

alright sorry lol

anonymous · Answer

continue :)

anonymous · Answer

$$6n + 9 = 81$$$$6n = 72$$$$n = 12$$

anonymous · Answer

So now you tell me the length of the hypotenuse!

anonymous · Answer

then if the hypotenuse is 12 then the other leg is 3ft longer so its 15?

anonymous · Answer

You got that backwards but yes. The hypotenuse is the one that is 3ft longer.

anonymous · Answer

got it now i remember the hypotenuse leg was always longer than the others

anonymous · Answer

I appreciate your time and your help

anonymous · Answer

:D (Give me a medal then :P )

anonymous · Answer

I wish i could lol

anonymous · Answer

Just click the "best response" thingy next to any of my posts.

anonymous · Answer

however your actions wont go unnoticed

anonymous · Answer

got it :)

anonymous · Answer

Good luck with your future mathematic endeavours

anonymous · Answer

thank you, I hate to bother you but I have one last math equation thats bothering me and ill leave you alone for the rest of tonight

anonymous · Answer

If it's a new question it's better to open a new topic. But I'll go there and help you.

anonymous · Answer

a room has a rectangular space of 230^2 for a square dining room and a 13ft wide kitchen. find both the width of the square dining room nd the length of the entire rectangular space

anonymous · Answer

I'm trying to figure out how that even makes sense.

anonymous · Answer

Ok, I think I get it.

anonymous · Answer

the length of the kitchen is 13ft and the area of the dining room is 230 square feet....its kind of hard to explain

anonymous · Answer

ok

anonymous · Answer

the dining room is 230 square feet and the width of the kitchen is 13ft

anonymous · Answer

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