the length of a rectangle is 4 times than its width. the area of the rectangle is 1024cm2

find
the length of the rectangle
the perimeter of the rectangle
4 square has the same perieter as that its rectangle. Find the area of the square.

I need to find the width

Length = 4 times width

Area = length * width
=(4w)w
=4w²

So 4w²=1024 cm² (given)
w²=1024/4=256
w=√(256 cm²)
=16 cm (reject negative value of square-root)

COOL ASWER

noice

Well, well, well! We have a rectangular situation here. Let's clown around with some math!

If the length of a rectangle is 4 times its width, we can say that L = 4W. Got it?

Now, we know that the area of the rectangle is 1024cm2. That means L x W = 1024. Since L = 4W, we can substitute it in and find our answer.

(4W) x W = 1024.

Now let's solve this circus equation. 4W^2 = 1024. W^2 = 256. That means W = 16.

Since L = 4W, we multiply 4 by 16 to find that the length is 64.

Now that we have the length and width, we can calculate the perimeter. The formula for the perimeter of a rectangle is P = 2L + 2W.

So, P = 2(64) + 2(16). That gives us P = 128 + 32, which is P = 160.

The perimeter of the rectangle is 160cm.

Now, let's move on to the circus of squares!

If 4 squares have the same perimeter as the rectangle, we divide the perimeter by 4 to find the length of each side of those squares.

In our case, the perimeter of the rectangle is 160, so each square would have a side length of 160/4 = 40.

To find the area of a square, we use the formula A = s^2, where s is the length of one side.

So, A = 40^2, which gives us an area of 1600 square centimeters.

Voila! We've clowned our way through the math circus and found the answers.

To find the length of the rectangle, we can set up an equation using the given information. Let's say the width of the rectangle is "w" cm. Since the length is 4 times the width, the length would be "4w" cm.

Since the formula for the area of a rectangle is length × width, we can set up the following equation:

Length × Width = Area
(4w) × w = 1024

Simplifying the equation:

4w^2 = 1024
Divide both sides by 4:
w^2 = 256

Taking the square root of both sides to solve for w:
w = √256
w = 16

Therefore, the width of the rectangle is 16 cm. To find the length, multiply the width by 4:

Length = 4 × Width
Length = 4 × 16
Length = 64 cm

So, the length of the rectangle is 64 cm.

To find the perimeter of the rectangle, we can use the formula: Perimeter = 2 × (Length + Width)

Perimeter = 2 × (64 + 16)
Perimeter = 2 × 80
Perimeter = 160 cm

Therefore, the perimeter of the rectangle is 160 cm.

To find the area of the square, we need to know the perimeter of the square. Since the perimeter of the square is the same as the perimeter of the rectangle, which is 160 cm, we can find the side length of the square.

Perimeter of square = 4 × Side Length

160 = 4 × Side Length
Divide both sides by 4:
Side Length = 40 cm

Now that we know the side length, we can find the area of the square by squaring the side length:

Area of square = Side Length^2

Area of square = 40^2
Area of square = 1600 cm^2

Therefore, the area of the square is 1600 cm².

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