.htaccess - htaccess with sub site

Question

I have an htaccess file under the main site

Options +FollowSymLinks -MultiViews

# Turn mod_rewrite on
RewriteEngine On

RewriteBase /

## hide .php or .html extension
# To externally redirect foo.php ot foo.html to foo
RewriteCond %{THE_REQUEST} ^[A-Z]{3,}\s([^.]+)\.(php|html) [NC]
RewriteRule ^ %1 [R,L,NC]

## To internally redirect /dir/foo to /dir/foo.html
RewriteCond %{REQUEST_FILENAME}.html -f
RewriteRule ^ %{REQUEST_URI}.html [L]

## To internally redirect /dir/foo to /dir/foo.php
RewriteCond %{REQUEST_FILENAME}.php -f
RewriteRule ^ %{REQUEST_URI}.php [L]

That works for

http://www.site.com/tenant-referencing/

but I can't get the subsite to work

http://www.site.com/newwebsite/tenant-referencing/

I have the same htaccess under the subsite

Thanks