Add Image Size for Featured Image with Responsive Design

You can wrap the image in a figure.

<!-- html -->
<figure class="constrained-container">
    <img src="https://wordpress.stackexchange.com/questions/100091/my-image.jpg" alt="What my image is about"/>
</figure>

Then style the figure as well as the image.

/* css */
.constrained-container {
    height: 300px;
    overflow: hidden; /* this hides excess of the image */
}
.constrained-container img {
    display: block;
    width: 100%;
}