I can see two ways to solve it:
<input type='text' name='dimensions' size='50' maxlength='75' value='<?php echo $dimensions1; ?>' />
// will output
<input type='text' name='dimensions' size='50' maxlength='75' value='1.72"W x 18"H x 3"D'>
The other way is to change the " sign to ". I think that is done with [man]htmlspecialchars[/man], but I'm not sure. Anyway the output will be the following:
<input type="text" name="dimensions" size="50" maxlength="75" value="1.72"W x 18"H x 3"D">
And that works as well.