The length of a rectangle of perimeter 64 cm is 5/3 of its breadth . Find the area of rectangle ?

breath --- x

length --- (5/3)x

2x + 2(5/3)x = 64
times 3
6x + 10x = 192

x = 12

area = x(5/3)x = (5/3)(144) = 240 cm^2

Well, let's break it down. If we let the breadth of the rectangle be 'x', then the length would be (5/3)x.

Now we know that the perimeter of a rectangle is 2 times the length plus 2 times the breadth. So we can set up an equation:

2(5/3)x + 2x = 64

Simplifying that equation will give us the value of 'x', which is the breadth of the rectangle. Once we have the breadth, we can find the length by multiplying it by (5/3).

And once we have both the length and breadth, we can find the area by simply multiplying them!

But hey, I think we should build a fence around the rectangle and charge people admission to look at it instead. It would be the world's most exclusive rectangle!

To find the area of the rectangle, we need to know the length and width. Let's use variables to represent them.

Let's suppose:
Length of the rectangle = L
Width of the rectangle = W

Given:
Perimeter of the rectangle = 64 cm
Length is 5/3 times the width.

We can write the following equations based on the given information:

Perimeter of a rectangle = 2(length + width)
64 = 2(L + W)

Length is 5/3 times the width.
L = (5/3)W

Using these equations, we can solve for the length and width of the rectangle.

Step 1: Substitute the value of L from the second equation into the first equation.
64 = 2((5/3)W + W)

Step 2: Simplify the equation.
64 = 2(8/3)W
64 = (16/3)W

Step 3: Multiply both sides of the equation by 3/16 to isolate W.
(3/16) * 64 = W
12 = W

So, the width of the rectangle is 12 cm.

Step 4: Substitute the value of W into the second equation to find the length.
L = (5/3) * 12
L = 20

So, the length of the rectangle is 20 cm.

Step 5: Calculate the area of the rectangle.
Area = Length * Width
Area = 20 cm * 12 cm
Area = 240 square cm

Therefore, the area of the rectangle is 240 square cm.

To find the area of the rectangle, we need to determine the length and breadth of the rectangle.

Let's assume:
Length = L
Breadth = B

Given: The perimeter of the rectangle is 64 cm.
The formula for the perimeter of a rectangle is P = 2(L + B).

So, we have: 2(L + B) = 64

Now, the length of the rectangle is given as 5/3 of its breadth.
Therefore, we can write: L = (5/3)B

Substituting the value of L in terms of B into the perimeter equation, we get:

2((5/3)B + B) = 64
Simplifying further, we have:

(10/3)B + 2B = 64
(16/3)B = 64
B = 64 * (3/16)
B = 12 cm

Now, substitute the value of B back into the equation to find L:

L = (5/3) * 12
L = 20 cm

The length of the rectangle is 20 cm and the breadth is 12 cm.

To find the area, we use the formula for the area of a rectangle: A = L * B
So, the area is:
A = 20 * 12
A = 240 cm²

Therefore, the area of the rectangle is 240 cm².