fix DropdownMenu overflow

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

@@ -905,9 +905,11 @@ class _RenderDropdownMenuBody extends RenderBox
     double? maxHeight;
     RenderBox? child = firstChild;
 
+    final double intrinsicWidth = width ?? getMaxIntrinsicWidth(constraints.maxHeight);
+    final double widthConstraint = math.min(intrinsicWidth, constraints.maxWidth);
     final BoxConstraints innerConstraints = BoxConstraints(
-      maxWidth: width ?? getMaxIntrinsicWidth(constraints.maxWidth),
-      maxHeight: getMaxIntrinsicHeight(constraints.maxHeight),
+      maxWidth: widthConstraint,
+      maxHeight: getMaxIntrinsicHeight(widthConstraint),
     );
     while (child != null) {
       if (child == firstChild) {
@@ -947,9 +949,11 @@ class _RenderDropdownMenuBody extends RenderBox
     double maxWidth = 0.0;
     double? maxHeight;
     RenderBox? child = firstChild;
+    final double intrinsicWidth = width ?? getMaxIntrinsicWidth(constraints.maxHeight);
+    final double widthConstraint = math.min(intrinsicWidth, constraints.maxWidth);
     final BoxConstraints innerConstraints = BoxConstraints(
-      maxWidth: width ?? getMaxIntrinsicWidth(constraints.maxWidth),
-      maxHeight: getMaxIntrinsicHeight(constraints.maxHeight),
+      maxWidth: widthConstraint,
+      maxHeight: getMaxIntrinsicHeight(widthConstraint),
     );
 
     while (child != null) {

packages/flutter/test/material/dropdown_menu_test.dart

@@ -2129,6 +2129,60 @@ void main() {
     // No exception should be thrown.
     expect(tester.takeException(), isNull);
   });
+
+  // This is a regression test for https://github.com/flutter/flutter/issues/147076.
+  testWidgets('Text field does not overflow parent', (WidgetTester tester) async {
+    await tester.pumpWidget(MaterialApp(
+      home: Scaffold(
+        body: SizedBox(
+          width: 300,
+          child: DropdownMenu<int>(
+            dropdownMenuEntries: <DropdownMenuEntry<int>>[
+              DropdownMenuEntry<int>(
+                value: 0,
+                label: 'This is a long text that is multiplied by 4 so it can overflow. ' * 4,
+              ),
+            ],
+          ),
+        ),
+      ),
+    ));
+
+    await tester.pump();
+    final RenderBox box = tester.firstRenderObject(find.byType(TextField));
+    expect(box.size.width, 300.0);
+  });
+
+  // This is a regression test for https://github.com/flutter/flutter/issues/147173.
+  testWidgets('Text field with large helper text can be selected', (WidgetTester tester) async {
+    const String labelText = 'MenuEntry 1';
+    await tester.pumpWidget(const MaterialApp(
+      home: Scaffold(
+        body: Center(
+          child: DropdownMenu<int>(
+            hintText: 'Hint text',
+            helperText: 'Menu Helper text',
+            inputDecorationTheme: InputDecorationTheme(
+              helperMaxLines: 2,
+              helperStyle: TextStyle(fontSize: 30),
+            ),
+            dropdownMenuEntries: <DropdownMenuEntry<int>>[
+              DropdownMenuEntry<int>(
+                value: 0,
+                label: labelText,
+              ),
+            ],
+          ),
+        ),
+      ),
+    ));
+
+    await tester.pump();
+    await tester.tapAt(tester.getCenter(find.text('Hint text')));
+    await tester.pumpAndSettle();
+    // One is layout for the _DropdownMenuBody, the other one is the real button item in the menu.
+    expect(find.widgetWithText(MenuItemButton, labelText), findsNWidgets(2));
+  });
 }
 
 enum TestMenu {