Suppose that a picture is 8 inches by 10 inches (width by height). You want to enlarge it so it is 20 inches wide. How tall will it be?

Cross multiply and solve for h.

Let h = height.

8/10 * 20/h

To determine the height of the enlarged picture, we can use the concept of ratios. The ratio of the width of the original picture to the width of the enlarged picture should be the same as the ratio of the height of the original picture to the height of the enlarged picture.

Let's set up the equation using the ratios:

(original width) / (original height) = (enlarged width) / (enlarged height)

Plugging in the given values:

8 inches / 10 inches = 20 inches / (enlarged height)

Now we can solve for the height of the enlarged picture.

Cross-multiplying, we have:

8 inches * (enlarged height) = 10 inches * 20 inches

Simplifying, we get:

8 inches * (enlarged height) = 200 inches²

Dividing both sides by 8 inches, we find:

(enlarged height) = 200 inches² / 8 inches

Simplifying further, we get:

(enlarged height) = 25 inches

Therefore, the height of the enlarged picture will be 25 inches.