`DropdownMenu.width` should support updating at runtime (#124847)

Fixes https://github.com/flutter/flutter/issues/120567

packages/flutter/lib/src/material/dropdown_menu.dart

@@ -648,6 +648,11 @@ class _DropdownMenuBody extends MultiChildRenderObjectWidget {
       width: width,
     );
   }
+
+  @override
+  void updateRenderObject(BuildContext context, _RenderDropdownMenuBody renderObject) {
+    renderObject.width = width;
+  }
 }
 
 class _DropdownMenuBodyParentData extends ContainerBoxParentData<RenderBox> { }
@@ -657,10 +662,18 @@ class _RenderDropdownMenuBody extends RenderBox
         RenderBoxContainerDefaultsMixin<RenderBox, _DropdownMenuBodyParentData> {
 
   _RenderDropdownMenuBody({
-    this.width,
-  });
+    double? width,
+  }) : _width = width;
 
-  final double? width;
+  double? get width => _width;
+  double? _width;
+  set width(double? value) {
+    if (_width == value) {
+      return;
+    }
+    _width = value;
+    markNeedsLayout();
+  }
 
   @override
   void setupParentData(RenderBox child) {

packages/flutter/test/material/dropdown_menu_test.dart

@@ -193,6 +193,28 @@ void main() {
     expect(buttonSize.width, customSmallWidth);
   });
 
+  testWidgets('The width property update test', (WidgetTester tester) async {
+    // Regression test for https://github.com/flutter/flutter/issues/120567
+    final ThemeData themeData = ThemeData();
+    final List<DropdownMenuEntry<ShortMenu>> shortMenuItems = <DropdownMenuEntry<ShortMenu>>[];
+
+    for (final ShortMenu value in ShortMenu.values) {
+      final DropdownMenuEntry<ShortMenu> entry = DropdownMenuEntry<ShortMenu>(value: value, label: value.label);
+      shortMenuItems.add(entry);
+    }
+
+    double customWidth = 250.0;
+    await tester.pumpWidget(buildTest(themeData, shortMenuItems, width: customWidth));
+    RenderBox box = tester.firstRenderObject(find.byType(DropdownMenu<ShortMenu>));
+    expect(box.size.width, customWidth);
+
+    // Update width
+    customWidth = 400.0;
+    await tester.pumpWidget(buildTest(themeData, shortMenuItems, width: customWidth));
+    box = tester.firstRenderObject(find.byType(DropdownMenu<ShortMenu>));
+    expect(box.size.width, customWidth);
+  });
+
   testWidgets('The menuHeight property can be used to show a shorter scrollable menu list instead of the complete list',
     (WidgetTester tester) async {
     final ThemeData themeData = ThemeData();