Javascript: Variable-sized image in fixed-sized canvas

Question

I have a fixed HTML5 canvas with dimensions 300x300. I'm resizing other images on the page to have maximum widths/heights of 300px (depending on which dimension is larger) via Javascript.

This doesn't actually resize the source images, though, and when I draw them on the canvas, the original size is used.

Is there a way to:

1. Resize these images with Javascript so that they're drawn to the canvas with a maximum height or width of 300px.

AND

2. Have the canvas retain its 300x300 dimensions with the resized image inside of it, so that a 300x300 square with the variable-sized image completely contained inside of it is created?

(Think making a 300x300 Photoshop file where you drop in various images and they resize to fit)

Is this even possible with Javascript/canvas?

EDIT

Here is the code I ended up using based on the accepted answer:

var ssItems = [exampleUrls], //array of image paths
imgHolder = document.getElementById("img-holder");

for (var i = 0; i < ssItems.length; i++) {
          var img = new Image(),
            imgSrc = "/ItemImages/Large/" + ssItems[i] + ".jpg",
            imgW,
            imgH;
          img.src = imgSrc;
          img.onload = function () {
              var canvas = document.createElement("canvas"),
                ctx = canvas.getContext("2d");
              canvas.setAttribute("class", "img-canvas");
              canvas.setAttribute("width", "300");
              canvas.setAttribute("height", "300");
              imgHolder.appendChild(canvas);
              imgW = (canvas.height * this.width) / this.height;
              imgH = (canvas.width * this.height) / this.width;
              if (this.height > this.width) {
                ctx.drawImage(this, canvas.width / 2 - imgW / 2, 0, imgW, canvas.height);
              } else {
                ctx.drawImage(this, 0, canvas.height / 2 - imgH / 2, canvas.width, imgH);
              }
            }

Answer 1

I have created the fiddle that tries to match the scenario explained above.

var canvas = document.getElementById('myCanvas');
var ctx = canvas.getContext("2d");

var image = new Image();
image.src = 'http://www.menucool.com/slider/jsImgSlider/images/image-slider-2.jpg';

// calculates width and height with respect to canvas
var width = (canvas.height * image.width) / image.height;
var height = (canvas.width * image.height) / image.width;

// takes width or height full choosing the larger value and centers the image
if(image.height > image.width){
  ctx.drawImage(image, canvas.width / 2 - width / 2, 0, width, canvas.height);
}else{
  ctx.drawImage(image, 0, canvas.height / 2 - height / 2, canvas.width, height);
}

You can take a look into it : https://jsfiddle.net/q8qodgmn/1/