Question

If wxyz is a square with wz =27, find rx.

Answer 1

Since WX is given as 27, we know sides of the square are 27 each.

ZX is the diagonal of the square. R is the midpoint of the square and also the diagonal. Thus, RX will be half of the diagonal (ZX).

The formula that relates a square's side length (s) to the diagonal length (d) is:

`d=s\sqrt[]{2}`

So, let's figure out the length of ZX first:

`\begin{gathered} d=s\sqrt[]{2} \\ ZX=WX\sqrt[]{2} \\ ZX=27\sqrt[]{2} \end{gathered}`

RX is half of ZX, thus,

`\begin{gathered} RX=(1)/(2)ZX \\ RX=(1)/(2)(27\sqrt[]{2}) \\ RX=(27)/(2)\sqrt[]{2} \\ RX\approx19.09 \end{gathered}`

Rounding to 1 decimal place, the answer is

RX = 19.1