Question

A square has diagonal length 13cm. What is the side length of the square

Answer 1

`(13 √(2) )/(2)` OR 9.19

Explanation:

hypotenuse =
`√(2)` * leg

13 =
`√(2)` * s

`(13 √(2) )/(2)`

OR (using pythagorean theorem)

`13^(2)` = 169

169 / 2 = 84.5

`√(84.5)` = 9.19

Answer 2

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{s}\\ o=\stackrel{opposite}{s} \end{cases} \\\\\\ (13)^2= (s)^2 + (s)^2\implies 13^2=2s^2\implies \cfrac{13^2}{2}=s^2 \\\\\\ \sqrt{\cfrac{13^2}{2}}=s\implies \cfrac{√(13^2)}{√(2)}=s\implies \cfrac{13}{√(2)}=s`