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xml - Android layout with square buttons

I want to make a layout similar to this one:

www.ImageBanana.net - layout.png http://www.imagebanana.com/img/9kmlhy66/thumb/layout.png

Four square buttons on the screen - each of those using half of the screen with/screen height (whichever is smaler). Independent of screen size/resolution.

I already tried to achieve this by using a LinearLayoutbut the buttons are ending up using the correct width, but still having the height of the background (not square any more).

<LinearLayout 
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="vertical" 
    android:layout_width="fill_parent"
    android:layout_height="fill_parent">

    <LinearLayout 
        android:layout_width="fill_parent"
        android:layout_height="wrap_content">

        <Button 
            android:layout_height="wrap_content" 
            style="@style/CKMainButton"
            android:layout_width="fill_parent" 
            android:text="@string/sights"
            android:id="@+id/ApplicationMainSight" 
            android:layout_toLeftOf="@+id/ApplicationMainEvent"></Button>

        <Button 
            android:layout_height="wrap_content" 
            style="@style/CKMainButton"
            android:layout_width="fill_parent" 
            android:text="@string/sights"
            android:id="@+id/ApplicationMainSight" 
            android:layout_toLeftOf="@+id/ApplicationMainEvent"></Button>

    </LinearLayout>

    <LinearLayout 
        android:layout_width="fill_parent"
        android:layout_height="wrap_content">

        <Button 
            android:layout_height="wrap_content" 
            style="@style/CKMainButton"
            android:layout_weight="1" 
            android:layout_width="fill_parent"
            android:text="@string/usergenerated" 
            android:id="@+id/ApplicationMainUserGenerated" />

        <Button 
            android:layout_height="wrap_content" 
            style="@style/CKMainButton"
            android:layout_weight="1" 
            android:layout_width="fill_parent"
            android:text="@string/tours" 
            android:id="@+id/ApplicationMainTour"/>

    </LinearLayout>
</LinearLayout>

It's looking like this: www.ImageBanana.net - layout2.png http://www.imagebanana.com/img/i2ni6g4/thumb/layout2.png

How can i acchieve the Layout to look like the image at the top above?

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import android.content.Context;
import android.util.AttributeSet;
import android.widget.LinearLayout;

public class SquareLayout extends LinearLayout {
    // Desired width-to-height ratio - 1.0 for square
    private final double mScale = 1.0;

    public SquareLayout(Context context) {
        super(context);
    }

    public SquareLayout(Context context, AttributeSet attrs) {
        super(context, attrs);
    }

    @Override
    protected void onMeasure(int widthMeasureSpec, int heightMeasureSpec) {

        int width = MeasureSpec.getSize(widthMeasureSpec);
        int height = MeasureSpec.getSize(heightMeasureSpec);

        if (width > (int)((mScale * height) + 0.5)) {
            width = (int)((mScale * height) + 0.5);
        } else {
            height = (int)((width / mScale) + 0.5);
        }

        super.onMeasure(
                MeasureSpec.makeMeasureSpec(width, MeasureSpec.EXACTLY),
                MeasureSpec.makeMeasureSpec(height, MeasureSpec.EXACTLY)
        );
    }
}

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