Question

one leg of a right triangle is 3 feet longer than the other leg. The length of the hypotenuse is 15ft. Find the length of the other two sides.
x^2(x+3)^2=(15)^2

Answer 1

i know that 3^2 is 9= and 15^2=225

Answer 2

\[x ^{2} + (x+3)^{2} = 15^{2}\]

Answer 3

you got that part right it looks like...

Answer 4

now solving for x?

Answer 5

having troubles with that?

Answer 6

yes im stuck i believe im missing a step to square i did the 3 and 15

Answer 7

hmm the whole (x+3) is squared... that means (x+3)(x+3) .... you have to foil it...

Answer 8

or expand it, however your text calls it...

Answer 9

remember how to do that?

Answer 10

im trying

Answer 11

k I'll check it when you're done

Answer 12

is it 2x+9....

Answer 13

x*x + x*3 + 3*x +3*3

Answer 14

x^2+x^3+3x+9

Answer 15

x*3 = 3*x I just put them in that order to help you to see how the expanding goes...

Answer 16

so x^2 + 3x +3x +9
(or x^2 +6x +9)

Answer 17

Is that clear? Have you worked with quadratic equations much?

Answer 18

this was the first lesson my professor breezed through it

Answer 19

do you see how I got x^2 +6x +9 from (x+3)(x+3) ?

Answer 20

yes you got x^2 by mult x by x... than 3+3 last 3 times 3

Answer 21

x*x is x^2 3*x is 3x another 3*x is another 3x and 3*3 is 9

Answer 22

so... I hope that's settled:) now we need to add the other x^2 we had in your equation
x^2 +x^2 +6x + 9 =15^2
2x^2 +6x +9 =15^2

Answer 23

yes that last line is where I left off and got stuck!

Answer 24

2X^2+6X+9=225

Answer 25

yes, now we have to solve for x
so set it equal to zero and either factor it or use the quadratic formula..

Answer 26

turns out it's factorable...

Answer 27

(x+12)(x ___) can you determine what goes in the blank?

Answer 28

what times 12 multiplies to the product of 225 right???

Answer 29

no, we set it equal to zero...
2x^2 + 6x +9 -225 = 225 -225 = 0
so it's
2x^2 +6x -216 =0
divide through by two:
x^2 +6x -108 =0
then factor:
(x+12)(x ___) =0

Answer 30

Sorry, I typed 'divide through by zero'
I meant "divide through by two" of course:)

Answer 31

(x-9)

Answer 32

good:)

Answer 33

so (x+12)(x-9) =0
x= ....?

Answer 34

-12 and...?

Answer 35

9

Answer 36

-12 and 9

Answer 37

yes. -12 is obviously not a useful answer here...
so x=9!

Answer 38

it's not useful because there cannot be any negative numbers?!

Answer 39

yes. it's the side for a triangle we can't draw. x=9 is the side for a triangle we can draw:)

Answer 40

thank you

Answer 41

sure! be sure to put the length of both sides in your answer one side is 9 and the other side is 9+3 ...
(you can verify that 9^2 +12^2 = 15^2 in order to check your work)

Answer 42

okay i did they said the answer was correct

Answer 43

great!