Answer:
BD = 32.5
Step-by-step explanation:
Since this is a square, the length of all the sides are equal. So line AB = BC = CD = DA = 23
Additionally, all the interior angles are the same (90°)
To find the length of BD, you can cut the square in half diagonally to form two right angled triangles, ABD and BCD.
For either one, BD is the hypotenuse of the right angled triangle so we can use Pythagoras' theorem to solve for the that (since we also know the legnth of the sides)
a = 23
b = 23
c = BD, which we have to find
[tex]a^{2} +b^{2} =c^{2} \\23^{2} +23^{2} =c^{2} \\\sqrt{23^{2} +23^{2} } = c\\\sqrt{529+529} =c\\\sqrt{1058} = c\\32.5 = c[/tex]
therefore the length of BD is 32.5
hope this helps!
