Question

find the two unknown lengths for: A right triangle has a hypotenuse that is 3 feet longer than one leg. The other leg is 4 feet.

Answer 1

Well, you know that for a right triangle\[a ^{2}+b ^{2}=c ^{2}\]
where a and b are the lengths of the sides and c is the length of the hypotenuse. If x is the unknown length of one side, how would you express the length of the hypotenuse?

Answer 2

\[x+3=\sqrt{4^{2}+x ^{2}}\]

Answer 3

3x=8+x^2?

Answer 4

No. The length of the hypotenuse would be x+3.
so you would have
\[4^{2}+x ^{2}=(x+3)^{2}\]\[4^{2}+x ^{2}=x ^{2}+6x=9\]Can you solve this equation for x?

Answer 5

that would be the one...ehehe

Answer 6

that should have been \[4^{2}+x ^{2}=x ^{2}+6x+9\]

Answer 7

x=7/6

Answer 8

yep, that is what I got.

Answer 9

yahp

Answer 10

That's it?

Answer 11

yes...simple

Answer 12

well, that gave you the length of the side, x
remember that the hypotenuse is x+3

Answer 13

then find the lenght of your hypotenuse which is x+3

Answer 14

25/6?

Answer 15

yes

Answer 16

so 7/6, 25/6?

Answer 17

That is the answer I got,

Answer 18

Yaaaaay! Thanks @pfenn1 @ren

Answer 19

you're welcome

Answer 20

welcome