math question4?

Question

two rectangles are similar. each of the rectangles is 3 times the length of the corresponding side of the small rectangle. how does the area of the large rectangle compare with the area of the small rectangle

Answer 1

i always do these by subbing in numbers.
Make the first rectangles length equal 1 and the width equal 2.

Make the second rectangles length equal 3 (3 times 1) and the width 2 (since it stays same)

2 times 1= 2
3 times 2=6

6 divided by 2 = 3
therefore the area of the larger rectangle is three times the smaller rectangle.

Answer 2

Similar rectangles means that the sides are proportional.

Say the small rectangle has sides a and b. The larger rectangle's sides are 3 times the length, so the sides are 3a and 3b.

To find the area multiply the two sides together and see how the two areas compare to each other.

Hope this helps. Good Luck.

Answer 3

Theorem: The ratio of the areas of similar polygons = the square of the ratio of corresponding sides. This says

A1/A2 = (s1/s2)^2 where A is the area and s is the length of a side.

In your case let A1 = area of larger rectangle and
A2 = area of smaller. Let 3x = side of larger rectangle and x = side of smaller rectangle. Then

A1/A2 = (3x/x)^2 = (3/1)^2 = 9/1.

This says that A1 is 9 times larger than A2. So the larger rectangle's area is 9 times the smaller rectangle's area.

I showed you this process because it works for all similar polygons. It may seem like a long way to explain it, but now you can apply it to many other problems that are like this one.

Answer 4

the large one is 9 times larger than the small one in area.

Answer 5

Hi

Try it out with a few examples and see if you notice a pattern.

K x

Answer 6

It is 9 times bigger.