# Math Help - Setting Up Equation

1. ## Setting Up Equation

I'm having trouble setting up an equation for this question, and would appreciate any help! I think I'll be okay once I have an equation, but I can't even get it started

A, B, C and D are posts on the banks of a 20m wide canal. A and B are 1m apart.
If OA is the same length as CD, find how far C and D are apart.

2. Hello, technology!

$A, B, C, D\text{ are posts on the banks of a 20m wide canal. }\;AB = 1$

$\text{If }OA = CD\text{, find }CD.$
Code:
            x
C o---------o D
\        |
\       |20
\   1  |
B o-----o A
\    |
\   |
\  |x
\ |
\|
o
O

Let: . $x = OA = CD.$

Note that: . $\Delta OAB \sim \Delta ODC$

So we have: . $\dfrac{x}{1} \:=\:\dfrac{x+20}{x} \quad\Rightarrow\quad x^2 - x - 20 \:=\:0$

. . $(x-5)(x+4) \:=\:0 \quad\Rightarrow\quad x \:=\:5,\:-4$

Therefore: . $x \:=\:CD \:=\:5$

3. Sorry for the late reply Soroban, but thanks for your help! It seems so easy now that you've explained it