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using minAreaRect you can find a RotatedRect for a line.

and you can change width or height of the RotatedRect

this is output of the code below:

#include <opencv2/imgproc.hpp> 
#include <opencv2/highgui.hpp>
#include <iostream>

using namespace cv;
using namespace std;

int main()
{
    // create a Mat
    Mat img(400, 400, CV_8UC3, Scalar(127, 127, 127));

    // 4 point for 2 lines
    Point2f pt1(100, 100), pt2(100, 200), pt3(300, 100), pt4(200, 300);

    // visualize lines and points
    line(img, pt1, pt2, Scalar(0, 255, 0), 2);
    line(img, pt3, pt4, Scalar(0, 255, 0), 2);

    circle(img, pt1, 2, Scalar(255, 0, 0), 2);
    circle(img, pt2, 2, Scalar(255, 0, 0), 2);
    circle(img, pt3, 2, Scalar(255, 0, 0), 2);
    circle(img, pt4, 2, Scalar(255, 0, 0), 2);

    // find RotatedRect for lines
    vector<Point2f> pts1, pts2;
    pts1.push_back(pt1);
    pts1.push_back(pt2);
    pts2.push_back(pt3);
    pts2.push_back(pt4);

    RotatedRect rr1 = minAreaRect(pts1);
    RotatedRect rr2 = minAreaRect(pts2);

    // change width or height of the RotatedRect
    if(rr1.size.width)
        rr1.size.height = 20;
    else
        rr1.size.width = 20;

    if (rr2.size.width)
        rr2.size.height = 20;
    else
        rr2.size.width = 20;

    cout << rr1.size << endl;
    cout << rr2.size;

    // Draw the RotatedRect
    Point2f vtx[4];

    rr1.points(vtx);
    for (int i = 0; i < 4; i++)
        line(img, vtx[i], vtx[(i + 1) % 4], Scalar(0, 0, 255), 1);

    rr2.points(vtx);
    for (int i = 0; i < 4; i++)
        line(img, vtx[i], vtx[(i + 1) % 4], Scalar(0, 0, 255), 1);

    imshow("RotatedRect Demo", img);
    waitKey(0);

    return 0;
}