You can nest the image in a 200x38 container, then set the max-width and max-height of the image to 100%. Here is a working snippet (I have included JS to make it interactive, but it is not necessary. Try resizing the container using the sliders):
var width = document.getElementById("width");
var height = document.getElementById("height");
var widthInput = document.getElementById("widthInput");
var heightInput = document.getElementById("heightInput");
var imageContainer = document.querySelector("div");
widthInput.addEventListener("input", function() {
width.innerHTML = this.value + "px";
imageContainer.style.width = this.value + "px";
});
heightInput.addEventListener("input", function() {
height.innerHTML = this.value + "px";
imageContainer.style.height = this.value + "px";
});
div {
width: 200px;
height: 200px;
border: 1px dashed #000;
}
.image {
display: block;
max-width: 100%;
max-height: 100%;
background: #333;
}
<div>
<img class="image" src="https://via.placeholder.com/400"/>
</div>
<br/>
<label>Width: <span id="width">200px</span></label>
<br/>
<input id="widthInput" type="range" min="0" max="400"/>
<br/>
<label>Height: <span id="height">200px</span></label>
<br/>
<input id="heightInput" type="range" min="0" max="400"/>
You can notice that however you change the dimensions of the container, the image is still contained within it. By setting the container to 200px wide by 38px tall, you can force the image to stay within the limits 0px ≤ width ≤ 200px and 0px ≤ height ≤ 38px.