geomerty but algerbra ???

[rhslaxer]

A-If RS=3x+1, ST=2x-2, and RT=64, find the value of x.
B-Find RS and ST.

i tried doin:
3x+1=64
3x=63
x=21
and
2x-2=64
2x=66
x=33
but i dont think i did what i needed to!!! please help

 

[Denis]

A-If RS=3x+1, ST=2x-2, and RT=64, find the value of x.
B-Find RS and ST.

If those are the sides of triangle RST, then not enough info is given.
Unless "greater than" is expected:
3x+1 + 2x-2 > 64
5x > 65
x > 13
If you can't follow that, only your teacher can help...

 

[soroban]

Hello, rhslaxer!

You suspected that it involved Geomtry.
Why didn't you make a sketch?

$\displaystyle \text{If }RS\,=\,3x+1,\; ST\,=\,2x-2,\;RT\,=\,64,$

. . $\displaystyle \text{(A) Find the value of }x$
.
. . $\displaystyle \text{(B) Find }RS\text{ and }ST.$

$\displaystyle \text{I suspect that the points }R,S,T\text{ are collinear.}$

          3x+1    S    2x-2
    R *-----------*-----------* T
      : - - - - - 64  - - - - :

$\displaystyle \text{We see that: }\;RS + ST \;=\;RT$

$\displaystyle \text{So we have: }\;(3x+1) + (2x-2) \:=\:64 \quad\Rightarrow\quad 5x - 1 \:=\:64 \quad\Rightarrow\quad 5x \:=\:65$

$\displaystyle \text{(a) Therefore: }\:x \:=\:13$


\(\displaystyle \text{(b) }\;\begin{Bmatrix}RS &=& 3x+1 &=& 3(13)+1 &=& 40 \\ \\[-3mm] ST &=& 2x-2 &=& 2(13)-2 &=& 24 \end{Bmatrix}\)