# Two rectangles are similar. If the height of the first rectangle is 3 inches, and the height of the second rectangle is 9 inches, how much larger is the second rectangle's area?

Area = width * height

Let us say the similarity is in the width. Call it 5 inches

A = 5 in * 3 in

= 15 in^2

======

A = 5 in * 9 in

= 45 in^2

======As you should have guessed the area of the second rectangle is 3 times as large as the first rectangle.

1 Person thanked the writer.
Tom Jackson commented
@Uh Huh

Turns out you were right.

HappyTo BeHereTo commented
The takeaway is that I'm a coward hiding in the background. I never argue about politics, religion or math.
Tom Jackson commented
Well, there apparently is no reality based reason for you to hide in the background about math.

In this case, John's answer was incorrect.

If the two rectangles are similar, then the ratio of the side of the 3 inch to the width of the 3 inch must equal the ratio of the side of the 9 inch to the width of the 9 inch

To state that mathematically 3/x = 9/y from which y = 3x for this "family" of similar rectangles.

So if x = 4, y = 12 and the area of one is 12 and the area of the second must be 108.

And if x = 5, y = 15 and the areas are 20 and 135

1 Person thanked the writer. 