Question

The length of the longer leg of a right triangle is
6inches more than twice the length of the shorter leg. The length of the hypotenuse is 9inches more than twice the length of the shorter leg. Find the side lengths of the triangle.

Answer 1

we need a variable, what do you pick?

Answer 2

x

Answer 3

ok then if the shorter leg is x, what is the longer leg? i.e how would you write "6 more than twice x"?

Answer 4

6+2x?

Answer 5

yes

Answer 6

and how would you write 9 more twice x?

Answer 7

9+2x

Answer 8

yes
now pythgoras

Answer 9

\[a^2+b^2=c^2\]so in your case \[x^2+(2x+6)^2=(2x+9)^2\]

Answer 10

multiply that mess out, combine like terms, and solve the resulting quadratic equation
you will get two solutions, ignore the negative one

Answer 11

Okay so 15?

Answer 12

yes

Answer 13

well the short one is \(x=15\)
the other two you find by replacing \(x\) by \(15\)

Answer 14

Thank you so much!

Answer 15

yw
solved that quadratic quick huh?

Answer 16

Longer is 36 right?

Answer 17

yes

Answer 18

and the hypotenuse is 39?

Answer 19

yes

Answer 20

you have \(15,36,39\) if you divide all by 3 you get the famous \(5,12,13\) right triangle

Answer 21

Thanks again! :)