The ratio of the corresponding side lengths of two rectangular tables is 4:5. What is the ratio of the perimeters? What is the ratio of the areas?

Ratio of Lengths

4:5

Ratio of Perimeters
4:5
(Remember you are adding sides proportional to each other; thus, the ratio will remain the same.)

Ratio of Areas
16:25
(In here, the ratio is squared. You may test with numbers if you wish.)

So the answer for what is the araes it would be 16:25

the ration of the corresponding side lengths of two simliar rectangles tables is 4:5

Oh, tables! The perfect place to gather for a feast or to have a heated debate about ratios. Let's get calculating, shall we?

The ratio of the corresponding side lengths is given as 4:5. So, let's assume the side lengths of the first table are 4x and 5x (for some value x), while the second table has side lengths of 4y and 5y.

To find the ratio of perimeters, we need to sum up the lengths of all the sides for both tables. The perimeter of the first table would be (4x + 5x + 4x + 5x), and the perimeter of the second table would be (4y + 5y + 4y + 5y). Simplifying these expressions, we get:

Perimeter of the first table = 18x
Perimeter of the second table = 18y

So, the ratio of the perimeters is 18x:18y. But hold on, we can simplify this further. Dividing both sides of the ratio by 18, we have:

Ratio of perimeters = x:y

Now, let's move on to the ratio of the areas. The area of the first table would be (4x * 5x), and the area of the second table would be (4y * 5y). Simplifying these expressions, we have:

Area of the first table = 20x^2
Area of the second table = 20y^2

So, the ratio of the areas is 20x^2:20y^2. But wait a minute, let's simplify this as well. Dividing both sides of the ratio by 20, we get:

Ratio of areas = x^2:y^2

And there you have it! The ratio of the perimeters is x:y, while the ratio of the areas is x^2:y^2. I hope this helped brighten up your ratios and tables journey!

To find the ratio of the perimeters, we need to understand that the perimeter of a rectangle is the sum of all its side lengths.

Let's assume the side lengths of the first table are 4x and 5x (where x is a common multiplier), while the side lengths of the second table are 4y and 5y. We can set up the equation:

Perimeter of first table = 2 * (4x + 5x) = 18x
Perimeter of second table = 2 * (4y + 5y) = 18y

Therefore, the ratio of the perimeters is 18x : 18y, which can be simplified to x : y.

Next, to find the ratio of the areas, we need to consider that the area of a rectangle is given by the product of its length and width.

The ratio of the areas of the first and second table can be expressed as:

Area of the first table = (4x) * (5x) = 20x^2
Area of the second table = (4y) * (5y) = 20y^2

Thus, the ratio of the areas is 20x^2 : 20y^2, which can be further simplified to x^2 : y^2.