Question

the shorter leg of a right triangle is 2cm less then the outer leg. find the length of the two legs if the hypotenuse is 10 cm. I thought I had the answer of 6 and 4 but evidently it is incorrect

Answer 1

Start with the pythagorean theorem:
\[a^{2} + b ^{2} = c ^{2}\]
where a is the shortest leg, b is the longer leg, and c is the hypotenuse.
Substitute the values into the pythagorean theorem and what do you get?

Note: a and b are a different variable in terms of each other.

Answer 2

ok

Answer 3

What is the equation you get?

Answer 4

I had x^2+(x-2)^@=10^2

Answer 5

the @ is supposed to be a

Answer 6

2

Answer 7

That's right, so you have to use the quadratic formula, right?

What were your steps there?

Answer 8

x^2+x^2-4+4=100

Answer 9

2x^2-4-96=0

Answer 10

2(x^2-2x-48)=0

Answer 11

(x-2)^2 doesn't equal x^2-4.

Answer 12

You have to expand it out, using FOIL

Answer 13

how do i do that my brain is numb now

Answer 14

FOIL stands for First, Outside, Inside, Last. So, when you have (x-2)^2, that means (x-2)(x-2).

Answer 15

x^2-x-2 2x+4

Answer 16

is that right

Answer 17

what is the x-2 2x part?

Answer 18

x times x and x times -2

Answer 19

and then 2 times x +2x and 2 times 2 equal 4

Answer 20

that + was supposed to be an =

Answer 21

\[(x - 2) (x - 2)\]
\[x^{2} - 2x - 2x + 4\]
\[x^{2} - 4x + 4\]

does this make sense?

Answer 22

so then you have to add that part... to the original equation. then you'll have a quadratic, so put that in the formula and solve.

Answer 23

ok

Answer 24

2x^2-4x-96=0

Answer 25

is that right

Answer 26

2(x^2-2x-48)=0

Answer 27

2(x+8)(x-6)=0

Answer 28

how am I doing so far

Answer 29

are you still there?

Answer 30

can someone please help me????????????????????

Answer 31

sorry I'm here. hang on

Answer 32

ok

Answer 33

Okay, so far we have:
\[x^2+(x-2)^2=10^2\]
\[x^2+(x-2)(x-2)=10^2\]
\[x^2+x^2-4x+4=10^2\]
\[2x^2-4x+4-100=0\]
\[2x^2-4x-96=0\]

Answer 34

Does all that make sense so far?

Answer 35

yes I have that

Answer 36

then I divided by 2 so it looks like this
2(x^2-2x-48)=0

Answer 37

is that correct

Answer 38

Yeah, you can do that... but it won't really help you very much. You're trying to solve, so the easiest thing to do is just to put that into the quadratic equation.

Answer 39

ok so how do I do that

Answer 40

Quadratic Formula is

\[\frac{ -b \pm \sqrt{(b^{2})-4(a)(c)} }{ 2(a) }\]

Answer 41

omg I don't know how to do that

Answer 42

hahahaha it's cool. It's easy! I'll walk you through it. So the a, b, and c stand for the different coefficients of the equation.

Answer 43

For this equation:
2x^2−4x−96=0
a=2 (for the x^2 component)
b= -4 (for the x)
c= -96 (for the x^0 component)

Answer 44

2 = a, 4 = b, 96 = c

Plug them in to the formula...

BAM your x is the result.

Answer 45

my bad forgot the negative signs, lol.

Answer 46

yea would have been ugly, without the negatives.

Answer 47

yeah pretty bad. so plug those in and what do you get?

Answer 48

that is where I am stuck

Answer 49

do one first with a + and do a second one with a - in front of the square root.

Answer 50

Lol yeah I wouldn't do that. solve the big ugly part first, and then you just add or subtract it.

Answer 51

You will get 2 answers, only one of the answers will be positive you have to use that one because you won't have a negative leg on a triangle.

Answer 52

http://www.mathwarehouse.com/quadratic/quadratic-formula-calculator.php

Plug in:

A = 2
B = -4
C = -96

Answer 53

but what is the equation i am suppose to use

Answer 54

heyyyy that's cheating!

Answer 55

(also, if you're going to do that... you might as well send him to wolfram alpha)

Answer 56

sorry, but she doesn't understand by what we are saying. She is probably in Elem. Algebra in college or in high school Algebra. They don't introduce the Quadratic Formula till the end of Elem. Algebra and sometimes the Beginning of Intermediate Algebra in College.

Answer 57

i just want to know what to do next so I can finish this ........ yes mat1033 college

Answer 58

Go to that site and plug in the info I said. Will show you the math.

Answer 59

I'm 55 and trying to get through this...... I knew I should have taken college and or statistics lol

Answer 60

Well, write it out, what it looks like when you plug in the numbers... and then I'll show you

Answer 61

idk what I'm plugging into I don't know what to do next. i thought I did:
2(x^2-2x-48)=0
2(x+8)(x-6)

Answer 62

I ended up with neg 8 and +6 so I thought the answer was 6,4 but the computer said no

Answer 63

yeah that's not it at all lol. He gave you the quadratic equation... which is:
\[(-b \pm \sqrt{b^2-4ac})\div2a\]
where
A = 2 B = -4 C = -96

Answer 64

I have never seen or learned that equation that you are showing.......... never mind I will just get it wrong. I need to go to sleep I have class tomorrow thanks anyway