Question

find the two unknown lengths. A right triangle has one leg that is twice as long as the other leg. The hypotenuse is 2 square root 5 inches.

Answer 1

Hint:

\[x^2 + (2x)^2 = (2\sqrt{5})^2\]

Answer 2

68?

Answer 3

\[x^2 + 4x^2 = 20\]\[5x^2 = 20\]\[x^2 = 20/5\]\[x^2 = 4\]\[x = \sqrt{4}\]\[x = 2\]

Therefore

short leg = 2
long leg = 4

Answer 4

Thanks Hero .

Answer 5

What about for: A right triangle has a hypotenuse that is 3 feet longer than one leg. The other leg is 4 feet.

Answer 6

The procedure is the same. Use pythagorean theorem and go from there.

Answer 7

Thanks .

Answer 8

Are you going to try it? If so, I'd like to see what you come up with for a solution.

Answer 9

I'm gonna try it .

Answer 10

Wait, what do i do first?

Answer 11

1. Write down Pythagorean Theorem: \[a^2 + b^2 = c^2\]

Answer 12

I suppose you want the second step instead.

Answer 13

3^2+4^2=c^2?

Answer 14

\[4^2 + x^2 = (x + 3)^2\]

Answer 15

Try your best to make sense of that and then let me know what the value of x is.

Answer 16

(x+3)^2 becomes x^2+9 right?

Answer 17

Hint:
(x+3)^2 = (x+3)(x+3)

Answer 18

x^2+9? lol

Answer 19

(x+3)^2
= (x+3)(x+3)
= x(x+3)+3(x+3)
= x^2 + 3x + 3x + 9
= x^2 + 6x + 9

Answer 20

That would be the Distribution/FOIL Method

Answer 21

I see... I've been doing math all day and now it's all confusing now.

Answer 22

I'm sorry to hear that. =[

Answer 23

Yeah, this is why i can't figure this out right now .

Answer 24

So are you telling me that you never learned how to FOIL?

Answer 25

Yes, I have learned FOIL .

Answer 26

Well, those steps I did above are FOIL. Maybe slightly different but only because I used a step by step procedure which involves distributive rule.

Answer 27

I even tried the foil and that's what i got too.

Answer 28

You tried FOIL and got x^2 + 9 ?

Answer 29

Actually i got x^2+6x+9

Answer 30

Oh, okay. Perfect! Now you can continue solving the problem =]

Answer 31

By doing what? lol

Answer 32

Oh wait i think i got this

Answer 33

1.5?

Answer 34

So after expanding the right side we have:

\[4^2 + x^2 = x^2 + 6x + 9\]

Now, just use basic algebra methods to solve for x.
Hint: Put like terms all on one side.

Answer 35

7/6?

Answer 36

Yes

Answer 37

So 6 & 7/6?

Answer 38

You'd be better off rounding 7/6 to a decimal.

Answer 39

6 & 1.16?

Answer 40

Where do you get six from?

Answer 41

I suppose you never understood how I came up with (x+3) to begin with.

Answer 42

Still confused....