Question

How do I find a and b?

Answer 1

I don't just want an answer... I need an explanation ...

Answer 2

By Pythagorean Theorem on the smallest right triangle, \[a^2+20^2=b^2\] However, using the biggest triangle, we have that \[29^2b^2=(21+a)^2\] This is now a solvable system of equations.

Answer 3

Alternatively, you can make a proportion using the fact that all of the right triangles are similar to one another.

Answer 4

That was really confusing.. @OakTree

Answer 5

What was? The first or second response?

Answer 6

Both of them...

Answer 7

@OakTree

Answer 8

For the first one, you can solve the system. Have you solved systems before?

Answer 9

No... I went from Algebra Support to Geometry.....

Answer 10

Oh! I see the mistake. In the first response, second formula, it should be 20^2 + B^2. Sorry.

Answer 11

Anyway, a system is when you have n variables and n equations, which allows you to solve for all of the variables.

Answer 12

You solve it by, in this one, taking the value for b^2 in the first equation and plugging it into the second equation. Because, b^2 is the same as a^2 + 20^2, so you can exchange them freely.

Answer 13

how did you get them squared???

Answer 14

You get\[29^2 + (a^2 + 20^2) = (21+a)^2\]

Answer 15

This is now an equation with one variable, which you should be able to solve pretty easily.

Answer 16

Oh, they're squared from the pythagorean theorem. You know, a^2+b^2=c^2?

Answer 17

oh okay!! I'm gonna try to solve that one and send you what I got as an answer/

Answer 18

Yeah I can't even solve that....

Answer 19

You've never solved a quadratic equation?

Answer 20

not that i remember

Answer 21

i thought i was supposed to put a/21=b/29?

Answer 22

That was the second solution. But then what do you do? You need a second equation, which you can only get from the Pythagorean Theorem.

Answer 23

then cross multiply?

Answer 24

this is so confusing.

Answer 25

You need to talk to your teacher. I can't teach you quadratics over OpenStudy...it's too complicated.

Answer 26

You're missing a lot of basic skills.

Answer 27

okay. thank you for the help.