You have two dimensions and you need to automatically change the second dimension when the first dimension is updated - to the same or to a derived value.
You can use dynamic text fields for such link. Create the first dimension in a usual way, by dimensioning an object. Create the second dimension, double-click on its text to edit it (use DDEDIT in older AutoCAD versions). Delete the original text (the dimension value) and choose Insert > Field from the context ribbon (or press Ctrl+F). In the Field dialog, choose the category Objects, the field Object. Select the the object of the first dimension and from the Properties list choose the property "Measurement". Adjust the Format and Additional format as neccessary and finish editing of the second dimension.
Both dimensions stay dynamically linked - the second one depends on changes of the first one (after regeneration or save).
Text fields can contain also arithmetic expressions (see the tip 9717), so you can also modify the text of the second dimension by a calculation.